it has a duration of an hour so as long as you maintain concentration then yes you can end your movement on a vertical surface or upside down

Silly question: does it have to be a live spider or could it be a dead spider that one might find in a dungeon or creepy basement or forest???

So Dhampir race recently came out, and this is 1 of the abilities of that race. I am now wondering, what are the limits of this spell? Mainly I am curious about the limits weight-wise, like how much weight could my character hold hanging upside down if they weighed 200 pounds? If I had to guess, I'd think something along the lines of how much weight they can carry plus the weight of my character.

Duration lasts for 1 hr. A turn is only 6 seconds.... end your turn you still have 59 minutes 54 seconds of wall clinging ability

no limit in spell, so go as crazy as your DM will allow

Yes and they can stay that way for up to an hour providing there is no interference to the spell caster or to the spell itself. 

What all is included as a "vertical surface"? Is a tree a vertical surface? Mountain side? Cave wall? Or are you limited to structures? 

@TheHolger
This is a clarification not a limitation. Humans naturally possess the ability to move across horizontal surfaces as do spiders. Yet you do not ( in most instances) have to determine whether or not the ground is stone, wood or a cave floor. Similarly a spider does not have to make the same clarification when crawling along a tree, a rock, or a cave wall. However I would say things like difficult terrain do apply. A mountainside could be craggy or jagged, a tree might be so small that there isn't much flat surface area to cling to with your feet. A cave wall could be covered in thick condensation or slippery moss. If it was nominal I would just say difficult terrain, so half movement, but if it were significant I might require an acrobatics check just like walking across a rope or slippery floor would do.

Quote from Schlermie >>

Does the Spider Climb spell still work on a wizard that wears a full-body gorilla suit that covers the hands and feet?

I would rule yes, as they would still be touching it through the suit without significant obstruction though it would probably vary based on the DM.

Also, context? Please?

verbal, somantic, and material, which are the components you need to cast this spell.

verbal means that you make noise casting it and can't cast it while silenced.

somantic means that you need at least one free hand to cast it.

material means that you need to either use a spellcasting focus, or provide the material stated in the description. you also cant use your spellcasting focus if it has a stated gp cost.

Yup. I love to cast this on myself, go up on the ceiling, cast burning hands, & incinerate my foes. 

“You Naruto run up the cliff shoot a arrow into the vampire’s heart and backflip back down” me after giving my ranger spider climb 

Quote from Schlermie >>

Does the Spider Climb spell still work on a wizard that wears a full-body gorilla suit that covers the hands and feet?

My gnome artificer uses his Steel Defender as a mount since it has 15 feet more movement speed than him.  One of my favorite things to do is use this spell to have the mount climb sheer cliffs.  
It's too bad that artificers have to wait until lvl 5 for 2nd level spells, though.