If I qualify in JEE session one, can I get admission in an NIT without writing session 2 of JEE?

Hi, Yes you there are chances that you can get admission in NIT if you have qualify in JEE session one but there should be good marks, so according to your score if you are eligible then you will get NIT or if you aren't then you won't.

Yes, indeed. NTA will declare results of JEE Mains examination based on the better of two principles. Meaning, if you appear for both sessions, your better marks in either of the sessions will be taken into account while declaring final ranking. So just don't worry. Best wishes to you.