Engineering

You need to score at least 150+ and above in MHT-CET to contest for a seat in MIT. That too, your branch of choice will hold the key to entry. Since 50% weightage is given to state board scores, your scores should be good there as well.
One needs to take the MHT-CET exam or JEE Main exam. Candidates

Bio Medical Engineering is a part of Electronics and Instrumentation !
80% of the syllabus is made up of Electronics and Math ! Rest is Biology!
PCB students are eligible for Bio Medical Engineering. Only at some private Universities like SRM University and Ramachandra University etc. My kind advice i

As you have not mentioned your home state I would consider only the OS quota in every college. You can get most of the NITs with your rank some of the picks would be :
MNIT Jaipur
VNIT Nagpur
NIT Rourkela
SVNIT Surat
MANIT Bhopal
NIT Raipur
These picks are mentioned in an order in which I would give them p

If you want to take admission on the basis of your class 12th marks so you should go for Thapar university or JIIT Noida. If you have percentage above 95 so you can confirm get admission into above colleges.

No it's not even possible to get admission into DU affiliated colleges also you can only get admitted in to private colleges

There is no option for government colleges in any of the branches even in lower branches also you will also not get admission into any private colleges also in CSE you can only get admission through management quota.

It's the worst branch of bhu instead you amcan take admission in CSE in other Pvt College.

Chances of getting Integrated M.Sc. Courses are high at NIT Warangal.

NIT Warangal is difficult. However possibility can be developed for integrated M.Sc. Courses. The following are the other options.
1. NIT Srinagar (Civil)
2. PEC Chandigarh (Civil)
3. NIT Andhra Pradesh (Chemical, Mech, MME)
4. NIT Hamirpur (MSE)
5. NIT Raipur (Chemical). .

Yes you can get. You can be hopeful for the following IITs.
1. IIT Dhanbad
2. IIT Jammu
3. IIT Varanasi.