Diploma

Yes they can Apply. There is separate entrance test for this available. Also u can get direct admission to few colleges if vacant seats are available there.

Physics chemistry and mathematics.

You should apply for entrance examination. There are many colleges in mp, wb and chennai

Yes, you can do this. The Lovely Professional University is offering B.Tech Lateral in Automobile engineering. The eligibility criteria is as under. Pass with 60% aggregate marks in Diploma (engineering. ). (any stream) 3 years after 10th or 2 years. After 10+2 (Non-Medical) or B.Sc. (Non-Medical) or B.Sc. (Computer Science) or equivalent, subject to qualifying LPU-NEST.

Yes, you can do this in DTU. The eligibility criteria at DTU for B.Tech lateral is three years engineering Diploma in any stream with minimum 60% of marks.

Generally, No. But, universities like DTU are allowing this. DTU eligibility criteria for B.Tech lateral is three years engineering Diploma in any stream. So, you can change here your branch.

The eligibility criteria of EPGC in Marketing Management IIM Kozhikode is as under.
A Bachelor's Degree or its equivalent in any discipline with minimum 50% aggregate mark or equivalent CGPA. and minimum 3 Years of managerial/ entrepreneurial/ professional experience after successful completion of graduation as on start date of the programme.
Admission criteria :- Admission to the programme is based on the Profile Evaluation & Personal Interview through video conference mode.
Programme Fee: Rs.2,20,000 + Taxes as applicable.
So you are eligible for this program.