Engineering Entrance Exam

Maybe, may not be. If you belong to the SC/ST category then you will get it. You will get integrated B.Sc-M.Sc if you are from general category. NIT, Patna, Agartala and NIT-Rourkela provide this course.
Hope it helped.
All the best.

You can take admission in the colleges like PEC College, Punjab University, etc.
And the JEE scores are dependent on the counselling procedure of the colleges.

It depends on you that in which course you want to take admission like:
Animation and multimedia
Writing and journal
Event management
First, check out on the internet which course you want to do then take a decision.

With this score, you will get none of the government colleges, you must try for private colleges.
Here a list of some good private colleges where can get admission:
1. Galgotias University
2. Shiv Nadar University
3. GLA University
4. GNA University
5. Oriental
6. LNCTE
7. RIMT
8. Satra College of Engineering

Yes, there are many colleges which can offer you admissions as you belong to SC category. Keep trying.

Yes, you'll get admission with your JEE Mains rank. Complete the online counselling process. You'll get choices of colleges all over India based on your JEE Mains score.

Always fill the CRL rank.
Admission committee doesn't need category rank they only need general rank and your category details. If the application form has a separate column for category rank, then you may fill it.

If you stay in Delhi, then you have bright chance og getting IIIT Delhi.