"We could jump across it as a last resort," Epee pitches

Barrows quest:

Kierro turns around. “Anyone here have [Tooltip Not Found]?(It’s supposed to say thieves’ tools)

Necromancer Quest: Kierro looks down at his amulet with Pelor’s symbol.

”...greet the sun with a smile... huh. I like it.”

Barrows quest: Asmodai will also look around for anything in the entry room:

Investigation: 7

He will also try to disarm the pit trap "You know, traps are kind of my specialty.":

Thieves' Tools:25

Necromancer's quest:

"You know Soar, on the bright side of your deity's focus, I hear that everyday people are just dying to get into the cemetery. I'd be happy to go along with you though to figure out this mess."

Barrows quest:

After (I assume) the trap has been disarmed, Dwaye walks through, though he moves quickly, just in case, once he gets to the other side he says ”Looks to be safe, come on, let’s try to finish this quickly so we can take another quest”

Necromancer quest:

”I’m down for some good ol’ fashioned justice”

Asmodai jams the trap door shut, it is now presumably safe to walk over it without triggering it (though you probably still try to walk around the edges, just in case).

"Oh, you're with them? I didn't mean to freeze you!" Epee tells Dwaye

Barrows:

Soar walks around the pit trap and moves into the next room, looking around. She looks for anything noteworthy in the room, and listens for any sounds coming from either door, and looking for any light or hint of movement (perception: 12).

---

Necromancer:

"Okay, the one condition I will put on my help for this quest and applies to anyone who comes along is that we need to behave. These are my coworkers and superiors and I'd really like them to respect me. This means no torturing. No lighting things on fire or rushing into new areas without checking with the party. That's not been our strong suit recently so I wanted to put it out there. Got it?"

Once everyone's confirmed, she will lead the party to Sir Ambrose. "Let's find out more about this necromancer, stop them, and permanently put to rest any skeletons we find."

Barrows Quest:

Soar looks at the doors; faint light is leaking out under the eastern door, and she can hear talking from both doors, though not enough that she can tell what is being said.

- - -

Necromancer Quest:

Soar leads the party to the City of the Dead, and there finds Sir Ambrose. "Ah, Soar, who are these friends of yours? Do they have business here?"

Barrows: Asmodai will also go to the next room, making sure there's no traps/secret doors around:

Investigation: 8

Perception: 6

Cemetery:

"I will be on my best behavior. Things will not burn because of me."

As a side note to Soar, Asmodai will whisper to her: 

"In your spare time, would you be willing to teach me about magic and casting spells? I'd really like to learn more about these things."

Asmodai finds no more traps or secret passageways.

"All's clear in this room guys..."

Assuming Asmodai also heard the voices: "but be quiet, there's voices here."

He will also listen to see if he can hear what the voices are saying at the door on the left.

Perception: 9

Barrows: Kierro listens to the door on the right.

Perception: 12.

Neither of you can tell what is going on, though Kierro thinks he hears the crackle of a fire. (Assuming by left and right you mean west and east, though it would be opposite from the party's perspective.)

Barrows:

Soar quietly says, "Hmm, this does not seem like a dungeon of undead things. Should we really go in and attack first? Should we ask questions first and then defend ourselves if they don't want to talk? I'm all for decimating undead that need to be put down. But I defer to the rest of you on what we should do if there are living things here." She suggests they slowly open the east (right on the map) door with the fire sounds and see what's there.

---

Necromancer:

Soar fidgets a bit, clearly a bit nervous about making a good impression in front of Sir Ambrose.

"Sir Ambrose, it's good to see you. We heard a story about a necromancer stealing bodies from this hallowed place to make a skeleton army. These new friends have agreed to help me stop that from happening. What can you tell me about it? Is anyone already looking into it? I don't want to step on someone else's toes, but I am certain that if we put our minds and arms to it, we can root out this scourge and destroy the skeletons for good."

She pointedly does not mention the manor or especially its ghostly bartender.

Barrows:

"I can peek in real quiet like, and tell you guys what I see and hear."

Necromancer Quest:

"Oh, well... It's true that we need help catching whoever has been desecrating our tombs. But, well, Soar, are you sure you don't want to leave this to a more seasoned man or woman of the faith? You are, well, you are still a neophyte as it is, aren't you?" It sounds like he could use some convincing.

Barrows Quest:

You open the door to the east, slowly.

Four goblins make merry around the fire, drinking copiously from a (stolen) keg of beer. A larger goblin, presumably their boss, is standing around, clearly in no mood for merriment. "Hey, you! What are you doing here? Did that elf tell you to come here?" He speaks with a sour tone when he mentions the elf.

Barrows:

(Soar is behind Asmodai and assumedly hears the goblin say this. If not, ignore the following. If so, she'll try to help with an attempt to get some information out of the goblins.) "What elf? We're here to help, but we haven't been working with any elf. We're looking into reports of evil spirits or undead coming out of this barrow. We'd like to destroy them. Can you tell us what you know about that? Would the elf know about that? Is the elf looking for undead?" (Persuasion: 18)

Necromancer:

"Oh, I appreciate the concern, Sir. But my friends here and I have proved fairly capable in a few quests we've undertaken, battling evildoers and helping others. And I've learned so much since I last saw you! Kelemvor has shown me how to channel his will into spellcasting and smiting. I do trust you on this, but I'm not the rookie you helped teach even a few weeks ago. That said, any advice you have for trying to right this wrong would be most welcome. And if you already have people from the chapterhouse on the case, why was there a call for help?"

Barrows Quest:

"I don't know if there's evil spirits here, we don't go down below but we haven't seen anything come up either. Anyway, that elf, I used to be the big boss around here but he forced his way in and now he's the boss of all of us. What's he down here for, I don't know, maybe he is looking to rob the tombs. Tell you what, if you want to kill the elf for us on your way down, I wouldn't get in your way."

Necromancer Quest:

"Very well, it is true we need what help we can get. Just please try your best to keep your friends out of trouble, this is sacred ground."

"Patrol the south side of the City of the Dead at night, I will be watching the north. Put to rest any living dead you should find, and your friends will be compensated for their efforts. If you should find who is responsible, doubly so."

Asmodai says to the Goblin, "How much would it be worth to you, should the Elf come to an early demise,  mein Freund?"

Erik to Soar and the rest of you guys; "Let's try for the double, yes?" Crossing fingers for all those investigation/perception rolls :)