JEE

You'll only get private colleges with this rank.

You have to pass the minimum criteria required to get admission through JEE Mains.

You might have a chance if you have any reservation criteria else give it a try. You have very great chance to get into this institute with this rank. Attend the counselling and choose your options appropriately. Try Shiksha college predictor for better analysis.

No, you can't get this college by other states quota. Because it's cut off is very high for others state students.

I am enlisting top colleges with their fee structure:
Centre For Environmental Planning & TechnologyAhmedabad-1,61,000
Lovely Professional University - 19500
Jadavpur UniversityKolkata-2,730
School of Planning and Architecture Delhi-46,300
NIMS UniversityJaipur-1,11,000
Sir J. College Of ArchitectureMumbai-17,800
Indian Institute of TechnologyKharagpur-74,000
National Institute of TechnologyThiruchirapalli-39,400
Jamia Millia IslamiaNew Delhi-64,500
Manipal UniversityManipal-3,04,000

I am enlisting top colleges with their fee structure:
Centre For Environmental Planning & TechnologyAhmedabad-1,61,000
Lovely Professional University - 19500
Jadavpur UniversityKolkata-2,730
School of Planning & Architecture Delhi-46,300
NIMS UniversityJaipur-1,11,000
Sir J. College Of ArchitectureMumbai-17,800
Indian Institute of TechnologyKharagpur-74,000
National Institute of TechnologyThiruchirapalli-39,400
Jamia Millia Islamia New Delhi-64,500
Manipal UniversityManipal-3,04,000

Go to Kotak or Indore otherwise Delhi will be good option for preparation of IIT-JEE. These cities have good atmosphere for study.

It depends from person to person. I personally believe that you should definitely drop for JEE. You know you are afraid that you may lower your marks, which has a very low probability of happening. But if you drop and do well next year, you could easily get a government college, which you have always wanted to and let me tell you, my friend, if you give your 100% next year, you shall get CS. You just can't let your fear stop you from trying. If now you let your fear stop you, then you are in a big trouble. Don't even think about marks, just go study.

Hello,
Yes, definitely you are eligible to take admission in private colleges for B.Tech degree in any stream of engineering. You won't get very good college with your marks and ranking but yes, you will definitely get a college for engineering. Go for counselling and get the private college.