Should I use the past tense for things that are still the same as before?

Yes, your first sentence should be in the past tense. The tenses of your sentences should agree. Maybe this year the number of Asian students has risen markedly, but it's not important now -- it might have been when you went there, though.

I wonder what kind of school you're talking about. Sounds like a college because you were already driving.

I'd revise the first sentence to read:

I went to an isolated rural college with very few Asian students.

I'm assuming that this was in an anglophone country, probably the USA (because of the car reference).

I'd revise the second sentence to read:

First semester, I had no car and did not leave the campus.

You don't want to sound helpless by saying that because you had no car, you couldn't go anywhere off campus. I added "isolated" to "rural" because, if you didn't leave the campus solely because you had no car, it means that there was no local town within walking distance and no public transportation. It's necessary to think a little bit more about the implications of what you say and how you say it.

Yes, that's right. The first sentence is fine because it's describing the situation that is still the same. The second sentence is right too.