Zalathorm wrote: »

Can you proceed with the main quests in dragonhold on a different character than you did the prologue without any issues unlocking achievements and whatnot?

Functionally, the Dragonhold main story is not connected to the prologue. There is no reason you can't do the Dragonhold quests on another character. I don't remember if the prologue had an achievement, if it did that won't carry over between characters. However, whether you've done the prologue on a character or not is completely independent of your ability to quest in that area.