Experience & drops
Is experience gain individual, divided/split between players, or
duplicated for each additional co-op player?
Each player gets the same experience. It is not split between them (like credits), but everyone gets the same amount (like ammo).
Do you get experience for others' work when you aren't in the same
area of the map?
You have to be relatively near an enemy kill (but not that close) to get the XP. (I think.) But quest experience is given no matter who turns in the quest and no matter how far away they are.
Do all players get the same quest rewards?
All players get the same rewards, with the exception if the quest gives different guns per class or random guns. If it's a single item, it will simply drop into your inventory if you weren't the one to turn it in. If there is a choice of items, everyone will get the mission accept dialog to choose their reward individually.
How are experience, difficulty, and item/money drops affected for each
additional co-op player?
I don't have exact stats, but there becomes more XP/items/cash and increased difficulty for each additional player.
Does the area difficulty scale to only the host's level, or does it accommodate/average difficulty between all players?
Host level, just like Borderlands 1. (You can twink low characters this way, as long as they don't get themselves killed everyone 10 seconds, I guess.)
Large level differences
Some games have disincentives when characters with large level
differentials play together—is that the case in Borderlands 2?
I haven't researched this, but I think the mechanic is similar to the way Borderlands 1 worked: meaning the XP is shared (not split) no matter your level.
Are higher-level characters' stats adversely affected when joining a
lower-level character's game? Or vice versa (boosting a lower-level character using a higher-level character's game)? Are experience gain or money/item drops diminished/impaired with large level differences? If so, what are the specifics?
It doesn't appear to alter the play stats or drops for differing levels. Basically, the host determines the level of enemies and drops, with number of co-op players increasing difficulty of enemies and amounts of enemies and item drops. (Though this isn't confirmed yet.)
Fight for your life time reduces each time you use it during a single 'fight'. It appears to reset once there are no aggroed enemies near you, or when you respawn at a New U.
Bleed-out time can be increased with artifacts, shield mods and some team-level bonuses. The number of players in the team won't affect it, but the number equipping Veritas gun or Aequitas shield will.
Player level and relative co-op level have no effect.
Best Answer
In my experience, when there are at least 3 players playing at the same time there can also be different enemy types that will spawn. For example in, The Highlands, near the row boat at the edge of the map a Badass Pire Thresher would spawn only if you had 3+ players in game.