Colleges in Vellore

Yes, irrespective of the branch.

BITS, Pilani's fees for B.Tech:
Semester fee: 132000
Admission fee: 32000
Hostel fee: 10000
Mess and other: 10500
Caution: 3000
Plus students union fee etc.
VIT Vellore's fee: 180000

Last form submission date for BITS, Pilani's BITSAT was 18th March 2018.
The last date of form submission for VIT, Vellore's entrance exam was 18th March 2018.

There is not much of a difference. But, I think the placement opportunities at VIT are slightly better than VIIT.

Let me explain you the admission system here. Rank in VIT to get admission should be 90,000, so you can get admission in VIT in the 6th category as well. There are various categories as well. With each category admission, the fee goes higher. The first category, closed till 15,000 rank and you can get CSE till 9000 rank and IT till 11000 rank, but there is a 2nd category as well, if you want CSE, you have to pay more for that.

Let me explain you the admission system here. Rank in VIT to get admission should be 90,000, so you can get admission in VIT in the 6th category as well. There are various categories as well. With each category admission, the fee goes higher. The first category closed till 15,000 rank, and you can get CSE till 9000 rank and IT till 11000 rank, but there is a 2nd category as well, if you want CSE, you have to pay more for that.
Hope this helps.

Yes, you are eligible, but you need to take VITEEE.

SASTRA University is the best option as it has better placement opportunities.

Yes, you can get admission, but the fee structure is high.