Right now, everyone (active members) can edit create tags but only mods and admins can delete them. I think this should be changed.

Who do you think should have rights to add tags? I would think it should only be voluntary and only to a selected group.

The next question I guess is, how can someone apply to be part of the tagging group? I can create a publicly 'joinable' group so members can add themselves voluntarily to the group and immediately get tag rights. Good idea?

With regards to finding out who created the tag, those with edit tag rights can edit the tags and can see who created them by hovering their cursor the specific tag.