. It has nothing to do with subjunctive mood. The verb of the dependent clause regresses with the main verb (would think...she was, would feel...there was), but may be retained in present tense if the condition still obtains now (would think...she is, would feel...there was). .
No. It's really not subjunctive. That would be ... think she were American. It's just a matter of the normal sequence of tenses. will think ... that she is ...
would think ... that she was ... If I wear these clothes, everyone will think that I am rich. If I wore these clothes, everyone would think that I was rich.