Most folks (well, me, in my experience) just bull on through the fire damage. They've either got the resists to survive it or the healing to overpower it long enough to murder whatever cast the spell. You can also hit either yourself or the caster (I forget which, but I'm fairly sure it's the caster.) with a ruination staff and dispel the fearscape effect, knocking you back into normal world. Not an option for an AM user, though. Generally, though, the lava floor doesn't do enough damage to kill you before you kill the enemy. Your best bet as an AM user would have been to pull AM shield up (would have reduced the fire damage) and possibly mana clash'd the giant, in the hope it drained its vim enough to break the spell (which has some upkeep to it, iirc).
As for fearscape's regularity, well, it's a corruptor talent. The player has access to it, too. You'll see it as often as you see corruptor class'd random unqiues or classed enemies that happen to have access to it. In my personal experience, though, you're not likely to encounter it more than a few times over a game. There's two guaranteed encounters with it, that I can recall (Grand Corruptor, shoeimp), but the rest comes from enemies with some classes tacked onto 'em.
Okay, probably maybe my last question for a while:
Do quests generally have any kind of time limit? A lot of the Alchemist ones so far have suggested so but I don't know if it's just flavor or actually a mechanic.
Only time time limits are involved in quests you'll actually have a little timer counting down on your status bar. Otherwise, there's no time limit. You can take as long as you want on the alchie quests.