Hello! Yes, you can use these interchangeably as both sentences are saying that the subject could be nervous. There is a slight difference, though, in the meaning of these two words - "seem" is used when something is "perceived" or "felt" almost on an instinctive level and "appear" would be used to refer to something that can be "observed" or "noticed". I hope that helps!

Yes they are different ways to say the same thing. You look nervous suggests the person looks nervous. You seem nervous suggests the person is acting nervous, may also be looking nervous. You appear to be nervous suggests the person is looking an/or also acting nervous and timid. Seem and appear are interchangeable they are all interchangeable, it is only personal preference, but looks suggests the nervousness is visible on the other persons face. If you use all three instead of always using /saying only one that would be the natural thing to do.