Subjunctive: Feelings/Opinions with present/past tense

[Roxerz]

I believe one of the rules with subjunctive is that feelings and opinions trigger subjunctive but can a present tense opinion be used with past tense subjunctive? I believe that in Spanish, if you use present tense, you must keep the whole sentence in present and past with past.

Also, the past tense subjunctive is used when something is no longer possible or isn't possible now but possible later?

I only know how to use them in "si" statements but don't know how to use them outside of the 2 examples below.
Si hubiera ido allá, lo habría conocido mejor
Si fuera rico, compraría un carro


I want to say, "It's weird that my Spanish professor is American and studied in Spain. She speaks very weird."

Es extraño que mi profesora de español sea americana y estudiera en españa. Habla muy rara