NIT

Tarun, yes with these marks you can hope of admission in some of the NITs. Also, with this score in 12th and JEE score you can get a seat in some of the best private universities which offer you admission on JEE scores/ tests conducted by them/ your marks in 12th. Some of these also offer good scholarships based on any one of the above mentioned admission criteria.

you need to get 95%+ in your 12th and the cut off marks for JEE Mains in 2015-16 batch was 109marks

288 in JEE Mains you can get into any govt college but not in IIT

No chance

Every engineering stream is good for girls now. However majority of girls prefer CSE, ECE or Biotechnology for engineering. BITS Pilani, Tapar , Manipal , VIT Universities are few other good options for doing engineering.

NIT's are very prestigious colleges and there cutoffs are usually very high. But for an estimation you can have a look at this -
https://edudrona.com/questions/question/what-ranks-should-i-get-to-secure-seat-in-a-nit/?mref=tanu