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I'm a 3.5 player, and in that edition there are two ways to Aid Another. The first in on skill checks, where the rules state " If you roll a 10 or higher on your check, the character you are helping gets a +2 bonus to his or her check, as per the rule for favorable conditions. (You can’t take 10 on a skill check to aid another.)".
The second is a combat action that states "If you’re in position to make a melee attack on an opponent that is engaging a friend in melee combat, you can attempt to aid your friend as a standard action. You make an attack roll against AC 10. If you succeed, your friend gains either a +2 bonus on his next attack roll against that opponent or a +2 bonus to AC against that opponent’s next attack (your choice), as long as that attack comes before the beginning of your next turn."
Following these, it's pretty easy to go through your list:
Just for reference:
d20 SRD said:
Aid Another
You can help another character achieve success on his or her skill check by making the same kind of skill check in a cooperative effort. If you roll a 10 or higher on your check, the character you are helping gets a +2 bonus to his or her check, as per the rule for favorable conditions. (You can’t take 10 on a skill check to aid another.) In many cases, a character’s help won’t be beneficial, or only a limited number of characters can help at once.
In cases where the skill restricts who can achieve certain results you can’t aid another to grant a bonus to a task that your character couldn’t achieve alone.
See also: Aid Another in Combat
Emphasis mine. ^
D20 SRD said:
Aid Another
In melee combat, you can help a friend attack or defend by distracting or interfering with an opponent. If you’re in position to make a melee attack on an opponent that is engaging a friend in melee combat, you can attempt to aid your friend as a standard action. You make an attack roll against AC 10. If you succeed, your friend gains either a +2 bonus on his next attack roll against that opponent or a +2 bonus to AC against that opponent’s next attack (your choice), as long as that attack comes before the beginning of your next turn. Multiple characters can aid the same friend, and similar bonuses stack.
Can you help Thief to pick a lock? - Yes, assuming you also make your lock pick check.
Unless the lock was of some kind of construction that actually
permitted more than one character to work on it, no. Also, by definition of the action, a character who couldn't pick a lock THEMSELVES cannot assist someone who CAN at doing so. And then you only need to roll 10 or better on the check to grant a +2 bonus to the lock picker. You don't need to roll against the difficulty of the lock itself.
Can you help Wizard to recall the name of that obscure cult? - Yes, assuming you also make your knowledge check.
Agreed, noting that knowledge is a trained-only skill. If you don't have skill points in the appropriate field of knowledge, you're not helping.
Can you help Cleric read his opponent in a charity poker tournament? - Yes, using the "Complex Skills" section to adjudicate the game.
Noting that this, too, would only be allowed if the character were permitted to communicate with the cleric, "I'm certain he's bluffing." Otherwise, the character would certainly have to be considered cheating - which has other consequences if detected, and detecting it would be certain if the players don't clarify that they are taking steps to not be detected at their cheating.
Can you help Fighter to spot the piercer before it falls on his head? - Yes, assuming you make the check and have time before it hits to warn him. I would typically make this the difference between a surprise round and normal initiative.
Again, if it's a spot check that the character is trying to help with, then they only need to roll 10+ on their own spot check in order to grant a +2 to the fighters own spot check - but that's unlikely since the "assisting" character is not going to be trying to help the fighter avoid danger (unless this has strangely been stated as being the case), but will be occupied looking for danger to HIMSELF.
If attempting to aid the fighter's attack roll or AC then the assisting PC need only roll to hit AC 10 to grant the fighter a +2 to hit (assuming the assisting PC can also attack the piercer) and in the case of boosting the fighters AC, the attack from the piercer then has to come before the assisting characters next turn (the AC assistance doesn't help if the piercer doesn't then actually attack within a timespan of 1r.).
Can Thief help Fighter sneak past a sleeping dragon? - Yes, assuming he makes a check. This would most likely be explained as making other distractions that obscure the fighters movement.
It'd almost certainly be smarter for the fighter to try to assist the thief, but otherwise, yeah, that works.
Can Cleric help Wizard make his save vs. poison? - No, that's explicitly a Heal check (the Heal check could be aided, though).
Agreed that it doesn't work, but not because it would require a heal check, but because a saving throw is simply not one of the ways in which Aid Another is stated to be beneficial. A save is not a skill check but a different kind of check entirely, and in combat Aid Another helps with an attack roll or to boost AC,
but not saves.
Can Wizard help Cleric to snap out of a hold person spell? - Hold spell, no. Sleep spell, yes.
Agreed.
Can Fighter actually do what he’s doing in the comic? - Depends on how the DM was running it. If it was a reflex save, no. If it was an attack against AC, yes. Spot against the pendulum, yes. Tumble? That's a little bit grayer, but probably yes.
If what the character is attempting to aid is a skill check, yes. If it's an ally's attack roll, yes. If it's an ally's AC against an attack roll, yes. Against anything else, no. And again, if circumstances are deemed to be such that the Aid can't help, then it can't help. For example, a pendulum whose game mechanics work by making an attack roll against the character might be deemed something that others cannot aid the victim's AC because they might not be able to affect the pendulum in any way that would help. Simply waving pompoms and cheering, "Go team! Go!" will NOT help improve anyone's AC. Maybe their MORALE depending on the attractiveness of the cheerleader...