Im trying to find out what the proper spelling of the Daedra Prince Vaermina is. Because i've seen it spelt Vaermina and Vaernima and I don't knowwhich is right. Help?

Both are right. http://www.uesp.net/wiki/Lore:Vaermina I believe Vaermina is the more commonly used spelling though.

Only a few in-game texts/books spell her name "Vaernima". All other places (including in-game dialogue in MW and OB, as well as the official sites online) spell it "Vaermina".