Are these sentences correct?
I have applied to the university.
I have applied for MA.
I think that we should use "to" with institutions but "for" when talking about jobs and courses. Am I right?

For me (or To me), studying at the university is a pleasant experience.
would you please explain to me what is the difference between "for me" or "to me" when I want to express what I believe or think.

Another issue,
We work hard to gain experience (or expertise).
Are these words interchangable?

Thank you for your help!