I believe there's a console command to bring up the race menu, so you can modify your faces, hair, or race. I have a question. If I use it just to change my hair or face, will it reset my stats or anything like that?

First, make a forked save before bringing up this menu. This can hose your character, but the full effects of the hosing is not apparent until you save and reload. Also, not all the changes you want will show up until you save and re-load, hence the forked save just in case. Note, this is not guaranteed to hose your character, just has a chance to.

showracemenu
shownamemenu
showsignmenu
showskillsmenu

Those are the ones I remember, but I think Race gets you all of the menus, where the others are just specific.

Yes. I think you're right about the ShowRaceMenu but don't use the http://www.uesp.net/wiki/Morrowind:Console#Enablestatreviewmenu command, because if you do then everything will be erased even the immunity for common disease, blight disease, corprus disease is removed from your character. Another thing that allows you change your character is to use mods for things like that and if you want to use mods then search for it with http://www.tessearch.com/.