Is it inappropriate for this person to behave like this when moving into my apartment?

Do NOT let her move in! Just ignore her calls, seriously. This woman doesn't want to be on the lease b/c she wants to be able to skip out on you whenever she feels like it. This is a disaster waiting to happen. And I'll tell you this, if she steals something from you, you won't be able to do anything about it because you let her live with you. Don't do it!