I believe the only time more than one character in a location can attempted a check is if the card requires multiple checks to defeat it.
With bains and barriers that require multiple checks I believe the rules state that the character who encountered the card must attempt and pass at least one of the required checks before another character can step in to attempt the next check.
I dont believe this can be done with boons, the character who encountered it must make the attempt to acquire the card and if not it is banished.
With blessings if it states "add X die to the check", its referring to the base die used in the attempt.
hope this helps
1. Only you can deal with the card you encounter. Others can help you, but you have to deal with it.
That being said, you asked about barriers like Heavy Chest. Most of those say you MAY banish the card if undefeated. If you are greedy enough and want to risk an extra turn, you can shuffle it back into the location deck like any other undefeated barrier. You don't HAVE to banish it, you MAY.
Some banes require multiple checks to defeat. They may say "Combat 10 THEN Combat 12". For that, the character that encountered the card has to make at least 1 of the checks, but another character at the location can handle the other check. You'll take damage from both failed checks against a monster in this case.
2. See above. These will help too:
http://paizo.com/paizo/faq/v5748nruor1gk#v5748eaic9ral
http://paizo.com/paizo/faq/v5748nruor1gk#v5748eaic9ram
3. Add the "base" die of the skill being used. So if a weapon says "roll your strength or melee plus 1d8" and you play a blessing you would add an additional strength or melee die. You do not add all the bonuses again. So, for example, if Valeros uses a weapon that says "roll strenght or melee plus 1d8" he would roll 1d10 + 3 + 1d8. A blessing of the gods would turn that into 2d10 +3 +1d8. For some items that don't use a skill, add the type of dice they do use.
See this for help: http://paizo.com/paizo/faq/v5748nruor1gk#v5748eaic9r4a
Sounds good. Now I am a bit confused about the value of having multiple characters at the same location. I was playing with Lini and she can explore more frequently than other characters, but her dexterity is not very good to pass checks on barriers. Intuitively I thought having another character at the location added the benefit that if they ran into a treasure then the thief could handle it. Could someone please explain why there isn't more "cooperation" between character cards?
Some characters are very much about cooperation. Take a look at Valeros, Lem, and Harsk. Spellcasters can also cast spells to help others (Cure, Guidance, Aid, and Strength are a few Base Set examples, there are others). And of course anyone can play a blessing on any check (as long as they follow the limit of one card type per check per PC) to help an ally succeed.
Lini had trouble with the barrier and didn't defeat it the first time? Now you know there's a barrier somewhere in the deck, and can ask Merisiel to come over and explore hoping to find the barrier. Or perhaps you can do better and use Augury/Detect Magic / Spyglasses to find where the barrier is and plan your explorations accordingly. But yeah, No One Else Can Take Your Turn for You is a cardinal metarule of the game.
In group play, the game actually makes you choose between the advantages of having multiple characters at the same location and the advantages of having characters spread out at different locations.
Two characters provide benefits to other characters at their locations (Valeros and Lem).
Two characters provide benefits to not being with other characters (Merisiel and Harks).
Some boon cards allow you to help other characters at your location. Some boon cards allow you to help characters at other locations.
Having multiple characters at the same location against villains that have multiple checks to defeat means that a character encountering a villain can go all out against one of the checks and leave the other check for another character at the location to also go all out against. (At least 1 villain so far is also more difficult if you encounter him with no other characters at your location.)
Spreading out to multiple location gives you the opportunity to temporarily close locations when the villain is encountered so that he cannot flee and you can win the game.
Some locations have rules punishing you for having multiple characters there (like everyone has to summon and encounter the monster that any other character encounters). I wouldn't be surprised if we see locations that punish you for being the only character there.
So there are pros and cons for both strategies. The best thing to do is look at the situation you are in and weigh whether it would be better to be alone or team up at that particular moment, at that particular location, for that particular villain, with the particular characters in your group, during that particular scenario.
Good luck!