When you run out of health points in Borderlands 2 you enter a 'Last Stand'-style mode, on your knees and able to crawl very slowly. If you manage to get a kill with your parting shots (or an enemy you set on fire/acid/shock burns down on its own) you can gain a second wind, reviving yourself with a bit of health.
Alternatively a team mate can revive you, similar to in other first person shooters (ie: Left 4 Dead)
If you are not revived in time, you will die and be reconstructed at your last New-U Station, for which you will be charged a reconstruction fee. The fee for respawning at a New-U station costs 7% of a character's money. For example, if the character carries $1,000, the fee would be $70.
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.)
Best Answer
I can't provide exact numbers, but I have noticed that the more ammo left in the clip, the bigger the boom and the higher the damage. So firing once and then throwing your gun will cause quite a bit more damage than throwing an empty gun.
The usefulness of this is balanced by the fact that any ammo in your clip is used up when you throw the weapon. So an almost-full clip will do more damage but it chews through your ammo in no time at all - and of course you have to actually hit your target for it to be of any worth.
Note that you can't throw your 'last' weapon - i.e. if you don't have enough ammo to do a proper reload, your character won't throw the weapon.
Edit - More info based on Ben Brocka's comments: The explosions appear to always be the same size but the damage is affected by the gun's Damage stat. It's a fair assumption that Gun Damage would be the relevant Badass skill, then. Experimental evidence with Badass ranks enabled/disabled would be useful to confirm this.
Additionally, if you throw an elemental weapon, the explosion will do damage of that elemental type (e.g. throwing a Corrosive weapon will produce a Corrosive explosion). Non-elemental weapons and explosive weapons both deal explosive damage.