[RPG] If a creature is lit on fire with burning hands, is it dealt damage automatically thereafter

RAW there really is only one option to quickly take off armor: have someone help you.

Getting Into and Out of Armor

The time it takes to don or doff armor depends on the armor’s category.

Don. This is the time it takes to put on armor. You benefit from the armor's AC only if you take the full time to don the suit o f armor.

Doff. This is the time it takes to take off armor. If you have help, reduce this time by half.

The fastest a PC could shed heavy armor with help would be in 2 and a half minutes or 25 rounds of combat.

RAW options to avoid the damage

1. Run away. As I interpret the spell you would still need to be in its range to use the bonus action attack. Running out of range would be difficult to achieve since the spell attack is a bonus action allowing the caster to use both their actions to follow you. However if allies impede the movement of the caster or your move speed is greater it could be accomplished in one round.
2. Deal Damage. Every time the magic user takes damage while concentrating on a spell they are forced to make a CON save to keep that spell up. If everyone hits the wizard odds are pretty high that he will fail one of those CON saves.

Houserule option

Let the PC take it off with a standard action, but doing so damages the armor, preventing them from wearing it again until they have it repaired.

Musings on Heat metal

There is no requirement for a PC or NPC whose gear is affected by heat metal to react taking off their armor. The stipulation of the spell is to throw it if they can, donning and doffing seems to be a bit more than all that and as such I would interpret it to mean weapons should be thrown, but armor can be kept on. I know 2d8 bonus action damage sounds like a lot, but dice only damage has a way of only coming out to be around the average most of the time, while 9 damage a round without an attack roll is pretty nice, it is probably a better idea for the party to focus-fire on the wizard to end it rather than someone in heavy armor taking their armor off and seriously lowering their AC for the rest of the fight.

The rules would have it do so, yes

The sorcerer’s elemental bloodline literally does nothing but swap the damage type of the spell; all other effects remain the same. In effect, an acid burning hands still launches a jet of flame and still sets things on fire – it’s just that the fire and flame now deal acid damage instead of fire damage. This can, of course, be easily justified as, “hey, it’s magic.”

Of course, seeing as acid’s effect is frequently described as a burning sort of feeling, this isn’t much of a stretch – the action to “put out the fire” could be “wiping the acid off” and “dousing” it could be “diluting” it. In most cases, “being on fire” is entirely equivalent to just “taking damage-over-time that you can use an action to end.” But then if you consider a spell that magically puts out fires – which would work – it gets a little tougher to explain.

It doesn’t have to be this way, of course. The DM certainly has purview to change something like this, and there is certainly room for adding variety this way. The problem is that the game does not define obvious substitutions to use; fire damage sets things on fire, but it’s less clear what the rest should do if you want them to all be distinct. Even setting up distinct damage-over-time effects is awkward – some spells douse fires, but there won’t be any spells that end these new damage-over-time effects that you make up.

Which is, of course, why the rules don’t do this: having a unique status effect tied to each energy damage type requires having the rest of the game react to that fact. Pathfinder doesn’t, and adding it now would be very difficult.¹ It’s much easier to say “it’s acid-damage-dealing fire, deal with it; magic, yo,” than to write out specific versions for each element, and then make sure they’re all reasonably competitive with one another, and that the rest of the product line takes into account, and so on.

1. ^{Remember, even when the elemental bloodline was written, much of “Pathfinder” was already “written” – the core rules did not change that much from 3.5, and most of 3.5 was just used as-is. A change like this would have required rewriting substantial portions of 3.5 that they chose to leave alone, and thus even at the “beginning” would have been very difficult.}