What are my chances of getting admission in NIT? Which NIT can I expect? Which engineering branch may get admission?

Sure, you can apply for MNNIT or NIT.

You get NITs like NIT-Bhopal, NIT-Patna, NIT-Jamsedpur, etc. You can also try for the remaining NITs and for better insight, refer to the google and search the previous year cut-off of NITs. You may get branches like ECE, electrical, civil, mechanical, chemical, etc.