Tomorrow, I will take my last exam of the semester and go back home. Tomorrow, I will take my last exam of the semester and go back home.

It might be more natural if you said "Tomorrow, I will take my last final and then go home". It's not wrong, but I think another American would say it like this. We always said "finals" when I was in college. The mid-semester exams were called "midterms".

I’m still trying to find a summer internship, and I’ve been hesitating for a long time about whether to change my major or not. I’m still trying to find a summer internship, and I’ve been hesitating for a long time about whether to change my major.

I don't think you need "or not"

I’m currently majoring in English, but I’m thinking of transferring to statistics. I’m currently majoring in English, but I’m thinking of transferring to statistics.

This sentence isn't wrong, but I would probably say "My current major is English, but I'm thinking about switching to statistics."

Since our school doesn’t offer a second major, the margin ofor error is much smaller. Since our school doesn’t offer a second major, the margin of error is much smaller.

"Margin for error" is fine but I "margin of error" is more common. Do you mean a double major?

Since our school doesn’t offer a secondallow double majors, the margin for error is much smallerI have to be decisive. Since our school doesn’t allow double majors, I have to be decisive.

"Margin of error" makes me think about surveys or statistics. I tried to naturalize your sentence. I've heard "double major" more than "second major" in the US.