B.Tech Computer Science and Engineering

CS and Me are actually like north and south. Both are very different in terms of scope, salary and types of jobs. But, if you want to earn high and need a very wide scope in future, then opt computer Science in this stream only you can get very much in limited amount of time. And, for more wide exposure, start preparing for GATE after the 2nd year.
I hope it helps. Best of luck.

MIT Pune is one of the best colleges in Maharashtra for engineering. It has high placement statistics with highest package of 14.32 lpa for Computer Science. Campus placements include companies like :-
Directi - 14.32 lpa
Barclays - 9-10 LPA
Morgan Stanley - 13.4 LPA
Deloitte - 6.5 LPA
You don't have to think much to choose this college.
All the best.

No, it will not be possible as the cut-off of BIT Mesra is a score of 150 and above.

CSE is good but mechanical and civil are the best branches.

It is a good choice. I would recommend, you should go through the syllabus of both IT and CS and have an overview of it. However, in my opinion, there is a little bit of difference in the syllabus of both.
All the best.

B.Tech computer science is a preferred branch in comparison to B.Tech IT because it's acceptance in the Indian and international market. If you have a choice then you must opt for B.Tech CSE over B.Tech IT.

You may go for BITS. It provides the best placement for CSE.

All private college having their management quota, it will depend on you where your quota application accepted or not.