Veermata Jijabai Technological Institute - VJTI Mumbai

VJTI ( Veermata Jijabai Technological Institute), Mumbai is a Government college and it takes admission through MHT CET only and only Maharashtra State students are eligible to take admission in this college.
if you belong to Maharashtra state then you should try to score more than 160 marks in MHTCET to get top branches in this college.
VJTI takes admission through MHT CET.
For CS branch you need to score more than 180 marks and for mechanical you need to score more than 175 marks in your exam.

You have to opt for JEE Mains paper 1, not paper 2 for B.Tech CSE in VJTI. You can get admission through JEE Mains paper 1 or MHTCET.
Details below:
https://www.shiksha.com/b-tech/course/b-tech-in-computer-engineering-veermata-jijabai-technological-institute-matunga-east-mumbai-81623

Yes, you can join diploma after 3 years but you have to give a proper reason in written why you had opted gap and your reason should be genuine.

You're chances are slim. Though you should apply to some other college as you're from st category you have chance to get some government college. All the best.

Yes, you should try applying. The results might surprise you.