Actually, everyone can mark Mobs, so it does not have to be the Tank or healer or whatever. I usually say everyone gets a mark, and puts it on a Mob he or she can CC for at least 30 seconds. A 8 second stun is no CC in my eyes.
Anyway, Everyone marks what he can CC, the first mob to die gets the targeting sign, the second the fire and then it does not matter anymore.
As for people running around, yes it is annoying and if my Resources allow it, I prevent them from dropping dead, but if I am below 70% I am not taking any chances, especially not on trash mobs, that is just humiliating to die on those.
My opinion, if you do not know the Instance/FP, you stick back, behind the Tank or whoever knows the area. If they write Wait, you wait, they most likely are typing about how to tackle the next encounter.
And for Petes sake, stop running around corners to evade your healers heals.