Admitedly, I am both new to being a DM and my adventuring group is made up of 4 new players as well.

The last few times we've gathered on a Friday night for gaming sessions (working our way through Dragon of Icespire Peak), I am noticing 2 repetitive trends with two of my players.  I think part of it is they are't 100% comfortable on how to play their characters or what to do in general as rpg's aren't normally in their wheelhouse, and I'm also sometimes stymied by their repetitive actions and feel they are let down (by expressions on their faces) when I gently turn them down.

Issue 1: I have a female bard/elf who as the game started at Lvl 1, started with her backgound story/origin as studying Arcana and lore at Neverwinter.  She wants to document the world and bring her findings back to publish or whatever.  Anyway, the party can't walk into a room, a clearing outside, a tavern, a hallway, anywhere...without her first action stating "Is there anything here for me to study?"  

I imagine throughout the campaign she will indeed discover a few things, and even some things I creatively throw in from time to time to appease her, but an example would be.  DM: "You turn a corner and find a hallway that has been carved out of rock by hand.  It is generally smooth, 10' in height, dirt floor. A few scant pebbles litter the ground.  There are no discernable markings.  It's a hallway."  Bard: "Is there anything here for me to study or write?"  (Repeat 100x).

Issue 2: Halfling Thief feels the need to steal/pick pocket EVERYTHING that isn't remotely essential to the overall game.  This player overall is having a hard time getting into character.  She admittedly states she's not creative, and I really have to nudge her moreso than anyone else to get her immersed in the game.  I believe she plays because her husband is also part of the group and she want's to be supportive and participate, but she's very comfortable of everyone else doing stuff and just following.  But when we get into generic rooms that don't have anything of any real value, I guess just to fill time or to say she is doing something, she'll ask if there's anything to steal.  Or if I say as a DM, (example) "You walk into the Tavern's kitchen.  They are between meal services now, with lunch having finished a bit ago and the few cooks that are here are clearly prepping veggies and meats for tonights offering.  Bard: "Are they on break or will they go on break soon?  Can I steal a spoon?"  This also happens many times and when I politely ask her to justify "Why do you need a spoon? (or whatever)" I am told "That's what thieves do!"  DM: Well, I suppose so, but wouldn't you rather try to steal something of value, something interesting, something I highlight as part of a mission?  Not everything that isn't nailed down has to be taken or of value.  

I feel this really slows the game down, but if I don't play along I can tell they feel a bit lost or unimportant.

Thanks in advance....

I have a female bard/elf who as the game started at Lvl 1, started with her backgound story/origin as studying Arcana and lore at Neverwinter.  She wants to document the world and bring her findings back to publish or whatever.  Anyway, the party can't walk into a room, a clearing outside, a tavern, a hallway, anywhere...without her first action stating "Is there anything here for me to study?"  

This is not a real problem. The player just needs to clarify the request. If a player asks me "Do I see anything interesting?" then I will ask back, "What sort of thing are you looking for, and where are you looking?" If they then say, "Doe the desk have any interesting documents in it?" then I would say, "Make an investigation check." If they make it, and there is something there, they find it. If there is nothing there, or they fail, they find nothing of interest. I usually describe it though, as in, "You find ink, some blank paper, some scraps of paper with untidy handwriting, and some order forms for pens dated 2 months ago" or similar.

I like the idea that her bard is wandering the world looking for things to write about, so as a DM, I would encourage this type of RP and try to put interesting stuff into the world for her to find and write about. But she does need to be clear -- you can't decide if what she is encountering is interesting enough to write about. She, as a character, must decide that. "Here is what you find -- do YOU think it's interesting enough to write about?" So -- ask for clarification ("what are you looking for, specifically?") and then provide details if she asks for something you can describe in the room. For instance in the tavern, she might say, "Well do I see any shady characters, people covering up their faces, that kind of thing?" and you would say "Make a perception check," and then if she succeeds, and someone has his hood up, tell her so. If not then say, "Nobody has their hood up or seems to be actively trying to conceal their identity."

On issue #2: This is a common problem with new players of thieves. They think that being a thief means "steal everything." It does not. For example on stealing the spoon, you ask why and she says, "That's what thieves do!"  No. It is not what thieves do. Thieves steal things of value to them for which they will gain a benefit that is worth the risk of being caught and punished. Stealing a random spoon from a kitchen is not something a thief does; it's something a kleptomaniac does -- someone who is not psychologically in control of the stealing impulse, and cannot control her own behavior. 

As for "slowing the game down," the only thing that matters is that people are having fun. If these 2 players are making the other players bored, and the other players are grousing, you need to have a group conversation about how this is a cooperative game and we need to keep the session moving for everyone. However, if nobody else at the table minds, I would submit that there is no rush... you don't have to have X number of battles per session or something. If the bard wants to RP wandering through the tavern collecting the patrons' stories, I see no reason not to allow it... Just keep cutting away to the other PCs and letting them do other things like RP with each other, haggle with the barkeep over prices, etc, so that the bard isn't the only one getting to play.

Honestly I think it's good that your players are getting into their characters, even if they seem to not really know exactly how to take advantage of those details. For the first player I'd say that you're reaching a point where your best bet is just to say, without rolling, "No, nothing of interest" and move on. It can be a tedious interaction to have every single time they enter a new room or location, but those times when they're able to find something of interest will make it worth the effort and keeps them engaged.

For the thief, I think I would try to encourage the player to start thinking about why their thief insists on grabbing something every room they're in. Are they a kleptomaniac who just desperately needs the rush of thievery? Are they just trying to get in practice when it doesn't matter so they're ready for when it matters? Are they an eccentric who loves shiny baubles regardless of their quality? Maybe they're actually extremely sentimental and want mementos to remember events by. I understand that the player is mostly just going, "Uh... thieves steal stuff, right? I'm gonna steal something". Don't pressure them too hard, but give them a few options and it might help them to get more into character and think about what they're doing.

Sounds to me like they both need to refine their characters. I think their motivations are too broad.

The Bard likely just needs a more focused topic to explain why they are adventuring and that you can feed as a DM. Maybe she is studying the behaviour of sentient undead as compared to their behaviour before undeath, or the social structures of different races that live in isolation, or she is tracing the lore of a particular enchanter’s works, or she is researching magical augmentation for the bardic profession. 

The thief is taking “thief” at its most basic: a kleptomaniac. You can probably do better, but you could roll with that and make it part of their bond and put mechanics around it. Maybe they they can’t control it and many have to save to not steal at in opportune moments. Better would be to consider different thief archetypes to give the player a directional focus: Robin Hood (hero), Butch Cassidy (burglar), Jesse James (outlaw), Bonnie and Clyde (psychotic), Charles Ponzi (schemer/conman), Danny Ocean (heists/conman), Al Capone (gangster), Indiana Jones (relic “collector”).

In both cases, I suggest you make the motivation heroic. Mundane will be a drag. 

Generally I agree with biowizard that this can be a good problem to have. They are trying to develop their characters, and you don’t want to stand in the way of that. But it can get annoying, so maybe you want to tamp it down a bit. In both cases, I’d turn it on the players and go with a version of “you tell me.”
If the bard asks if there is anything to study, you can calmly tell them you just described what they see, it’s up to her to decide if any of those things are worth further study. You shouldn’t be telling her what her character finds interesting, she needs to decide that for herself. 
As for the thief stealing, there’s a few options. First, if she asks if she can steal a thing, the answer I generally give is, you don’t know, you only know you can try, do you want to make a roll. Then start having there be consequences for the theft: they are spotted and it starts a fight, or someone calls the city watch, or it turns out that spoon belonged to the mayor, and boy is she mad now. You might even warn her, in advance, out of character, that this is something you plan to start doing, and that she should be a bit more discerning about what it is she’s going to pick up, is the risk worth the reward. 

If the bard asks if there is anything to study, you can calmly tell them you just described what they see, it’s up to her to decide if any of those things are worth further study. You shouldn’t be telling her what her character finds interesting, she needs to decide that for herself. 

Yup, this, and explain it politely to the player. "I can't decide if Victoria finds something interesting... you need to decide that. I can only tell you what is in the room."

Quote from BioWizard >>

If the bard asks if there is anything to study, you can calmly tell them you just described what they see, it’s up to her to decide if any of those things are worth further study. You shouldn’t be telling her what her character finds interesting, she needs to decide that for herself. 

Yup, this, and explain it politely to the player. "I can't decide if Victoria finds something interesting... you need to decide that. I can only tell you what is in the room."

 Of course, to help her you could embellish some of the descriptions with additional details that she will automatically make note of, without her having to ask "is there anything interesting".

I agree with the general consensus so far: this doesn't have to be a problem, but instead an opportunity for growth/refinement. Just a simple conversation with them at the table before the session to express your concerns, get their feedback, define some better motivations from them, get mutual agreement, and have fun!

Implicitly, new players are looking to the gm to run the game and *show* them how to play (even of the gm is as new as they are). There's also no *wrong* way to play, but showcasing/explaining how it can be played *differently* (that is, with better defined expectations, motivations, backgrounds) can enhance the in-the-moment verisimilitude of the game. Asking them to explain *why* places the discernment back on the player on behalf of their own character. 

If the players are truly invested to continue similar behaviors moving forward, another possibility is to ask the table if they'd be okay with devoting a half session to each player to explore these impulses (and giving the other players not yet discussed the option to have similar focus moving forward at their own discretion). The bard can spend time doing research at a library reconciling obscure and contradictory legends. The thief can plan and execute a heist. The other players can still participate in these shenanigans, provide support, or do other things. Even spending 10 full minutes on just one player (in just my personal opinion) doesn't ruin anyone else's fun. And "cut scenes" going back and forth between different activities is a great way to keep different things moving along so everyone stays engaged. That, though, is highly dependent on your personal comfort as the gm in juggling the back and forth madness, and all the player's buy-in on running a session or two in such a manner.

Returning to your original question though, i think you identified the hangup perfectly. The new players aren't fully knowledgeable or comfortable on what a  character is or what they can do. They sound like they're taking a very One-Dimensional approach. Discussing with them *exactly* what they want to accomplish is key. I doubt the bard wants to write a 50 volume encyclopaedia on everything/anything, so what's a more specific interest? The thief could just be a kleptomaniac (I guess that's fine??), but a good/professional thief is much more selective on what to steal, how, where, and why. 

Returning to your original question though, i think you identified the hangup perfectly. The new players aren't fully knowledgeable or comfortable on what a  character is or what they can do. 

I think this is a very important point.

If you think about the "thief" player, it seems like her whole character concept is, "I'm a thief; I steal things." But the class is not the character -- it is only one aspect of the character. Just like in real life, if you have a job, it's not "I'm a book-keeper, I add numbers." Being a book-keeper is one aspect of who you are, and for most people, not close to the most important one. Just like the book-keeper might have a husband, children, a house to maintain, a hobby of playing D&D, and volunteer work that she does on weekends, so too the "thief" character should be more than just a thief. Why does she steal, vs. all the other ways to earn a living? How does she feel about stealing? Is she ashamed of it? Or proud of being a good one? Has she had run-ins with authorities? What does she think about the authorities? Does she grudgingly respect them, like most of the murderers in a Columbo episode respected him by the end of the show? Or does she have outright disdain for them? And for either of those things, why?

The more of these kinds of questions she thinks about, and eventually answers, the more her character becomes a character instead of a class.

Quote from BioWizard >>

Returning to your original question though, i think you identified the hangup perfectly. The new players aren't fully knowledgeable or comfortable on what a  character is or what they can do. 

I think this is a very important point.

If you think about the "thief" player, it seems like her whole character concept is, "I'm a thief; I steal things." But the class is not the character -- it is only one aspect of the character. Just like in real life, if you have a job, it's not "I'm a book-keeper, I add numbers." Being a book-keeper is one aspect of who you are, and for most people, not close to the most important one. Just like the book-keeper might have a husband, children, a house to maintain, a hobby of playing D&D, and volunteer work that she does on weekends, so too the "thief" character should be more than just a thief. Why does she steal, vs. all the other ways to earn a living? How does she feel about stealing? Is she ashamed of it? Or proud of being a good one? Has she had run-ins with authorities? What does she think about the authorities? Does she grudgingly respect them, like most of the murderers in a Columbo episode respected him by the end of the show? Or does she have outright disdain for them? And for either of those things, why?

The more of these kinds of questions she thinks about, and eventually answers, the more her character becomes a character instead of a class.

Combine both concepts for an interesting character. The bookeeper/thief. Embezzlement is a trickier and less noticeable form of theft so long as you are the only one keeping the books and no one is auditing