Computer Science and Engineering

BCA is the right and best option. Also, you can do B.Sc in computer science. B.Sc and BCA have slight difference like, B.Sc mainly focuses on mathematical and the theoretical foundations of computing, whereas BCA course is a professional course designed for IT industry.

GATE has three benefits:
1. Entry to PSUs.
2. Entry to top level institutes for M.Tech.
3. Scholarship of 12000 per month, if you take admission in Government College for M.Tech.
But, your GATE score must be good to get any of the above.

Aerospace Engineering is niche branch of engineering with limited scope and job opportunities in comparison to IT branch. But it is a very interesting branch with lot of innovation and research. If you want to work on cutting edge technologies then you may prefer aerospace engineering over IT.

You need to qualify JEE Mains exam with good marks to get admission in NIT for CSE.

It depends on the school. Different schools have different criteria depend on the number of students and infrastructure available.

Amrita University and Karunya University are decent options.

You will have to approach the college administration.
Its easy to get a lateral entry.

It depends on the branch you want.
Tell me about the branch you want then i could further tell you.