Colleges in Tamil Nadu

Yes, you can join some colleges but some colleges set the criteria that they can take students only who got above 70% marks in class 12th. But some colleges will take the students who have above 60 percent marks too.

Yes, you can definitely get admission in Coimbatore Institute of Technology (CIT). For BE in Information Technology (IT) with the cut-off of 190.75. While taking admission class 12th percentage is also calculated.
Best of luck for your future.

You'll get a good branch in NIT, don't go for VIT. Though, getting into CSE of Manipal is a big chance. It is really great there. Moreover, other than CSE, you'll get other core branches easily with good NITs. Again, either get into Manipal or Amrita CSE or into other core into the good NITs.
Best o

Yes, you can apply to MIT.

It's a five-year integrated honours programme. Admission is based on merit (+2 marks and CLAT score).

If you have cleared JEE Mains then you definitely chances are there. Keep on trying.
All the best.

SASTRA would be a better choice as it has great placement record and is a "Deemed to be University".