JEE

you can get ti know about that online from the site itself.

Yes, you are eligible to apply for JEE Main 2020 (minimum 50% marks in PCM). To get admission in NIT, a candidate must secure at least 75% marks in 10+2 Exam (65% for SC/ST category) or be in the top 20 percentiles in the 10+2 exam conducted by respective boards.

If you are from general category ,you are not qualified for JEE Adv exam 2019.But that is not the end of the road. Everyone who appeared for Jee Mains are qualified to participate JoSSA counselling which are scheduled to be held after JEE Adv result .Even person at the bottom i.e having Zero percent

Please visit this link:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

Following colleges in Bangalore could be the best for you.
1. Christ University
2. PES University
3. REVA University.

Yes, you can get a good private college for engineering.

Check this college comparison tool provided:
https://www.shiksha.com/resources/college-comparison.

Chances are good. Apply for it.

Try to improve your percentile in next JEE Mains exam. You may get seat in upes ( good branch ) but try to improve for better result.

Congratulations for scoring good percentile in JEE. According to your score, there may be chances of getting a seat in this college.