Engineering

All courses abroad or specialized one. You can do PG Diploma or PG in:
Construction management
Structural engineering
Geo technical engineering
Go through few university website and see the course options.

Hi,
https://mhtcet2019.mahaonline.gov.in
Check out the link and compare it to last year's cutoff. Mostly you need to be in Top 100-200 for COEP.

Have you applied for any colleges?

Yes, you can take admission into M.Tech course without GATE score card. You can take admission in state technical university affiliated colleges by appearing for an entrance exam conducted every year by respective state university/colleges etc.

Clear GATE exam, apply for the college/PSU if you clear the cutoff you will receive call for the same.

Yes, it is possible, if you work hard and get a decent score in GATE. I think you can wait and you may get a chance in any of the good NITs.

Deeply clarify what actually you want to make your career. If it's maths, go for M.Tech. It's a higher qualification than any M.Sc. It gives easy placement and better job prospects.

Both are similar, but B.Tech=BCA+MCA. B.Tech duration= 4 years and BCA+MCA duration= 5-6 year. So, I suggest you can pursue B.Tech. But Im always suggested to do B.Tech CSE, it has more demand than MCA.

It is B.Sc in computer Science and over this score it is very difficult to get admission in DU. For you I am attaching the official link of the department of computer Science, Delhi University. You can visit this link. http://cs.du.ac.in/programmes/bsc/
This article will help you. https://www.shiksha

Yes, you can take admission in IITs. You have to qualify JEE Advance in order get admission there.