I wrote this sentence:
I choosed XXX University not just because it is a well-known university in the scientific community and its highly valued education, but...
I don't know if and is grammatically correct.
I think you're trying to say something like "not only because of A and B, but also Z".
Here is my suggestion (I changed your wording a little, but tried my best to convey the same meaning):
And joins constituents which play the same syntactic role.
The sentence you have written may be reduced to
In that construction, both A and B must be able to serve as complements of because. Because takes a clause as its complement:
But because cannot take an NP as a complement; with an NP you must use because of.
Consequently, you need to rewrite your sentence so your A and B are syntactically parallel:
The sentence isn't correct. You should use "but" here because of the negation (the "not"). "Not X but Y" or "not just ("only" is also common here) X but also Y" are common constructions in English. (We use "and" in an "X and Y" construction.) Also, choose is a "strong" verb; the correct past tense is "chose", not "choosed". So:
I wouldn't add anything to this sentence, so I left your "but..." off of the end. Now, here's how you could use "and":
As you can see, taking the "not" out of the sentence allows you to use an "X and Y" construction. This is of course also common.