"So, what do you think, should we give PC's the tools to run quests and grant a reward?"

No. Make them quest wizzies, and disallow them from having a player character at the same time. That's the best way. Then you also weed out anybody who just wants the powers, and it's more likely the ones applying actually are interested in making quests.

"A lot of it of course would be based on faith, ie, abusing the ability to go invis when you werent runnign a quest would be a bad thing, as would morphing when not running a quest, etc."

Yes. Rid, no questions asked, if using them when not running a quest would be a minimum punishment, if players are allowed these powers.