Is it "vita" or "vitae"? Why?
Vita means life. Vitae is the genitive (possessive) form, of life. Curriculum means something like course.  So Curriculum vitae means the course of one's life, and makes good sense. Vita by itself also makes good sense, though it's perhaps less accurate as a description of the document in question. Neither curriculum vita nor vitae without curriculum makes sense.

Addition, suggested by Patricia Shanahan: All the words in bold italic are Latin.