She looks as if she is rich = Her appearance suggests that she probably has a lot of money (maybe she is wearing expensive clothes, diamond jewellery, Jimmy Choo shoes).
She looks as if she was rich = I can't really think of a situation where I would say this. It suggests that she looks (now) as if she was (used to be) rich, but I can't really imagine how someone would give the impression of having been rich in the past but not rich now.
She looked as if she was rich = this is simply "She looks as if she is rich" but reported as a past event.
Student or Learner