JEE Main

50% is a must in every PCM subject and 75% in DTU.

The JEE Mains cut-off for general category is 51000.

Yes, you are eligible to get into DU with this score. However, the general category cut off for JEE this year was 100, thus you have to score more marks in JEE next year if you desire to get into good engineering colleges.

If you want to pursue petroleum engineering without JEE, then you can give state exams conducted by various institutes offering this course. For e.g. UPES university has separate exam for admission into the engineering courses. You can give this exam and get admission into petroleum engineering.

You can refer links below :
https://www.shiksha.com/10-tips-towards-your-jee-mains-advanced-preparation-article-11721-1
https://www.shiksha.com/jee-mains-preparation-tips-exampage

No, you need at least 75% in 12th standard for the same.

Dear,
Kindly, prepare for JEE as you do not need to attend the class 12th exams. Put your best efforts to prepare for the same. Prepare for your weak topics. Take suggestion from best teachers and use all the online available facilities. Avoid all your fears. Learn all the required formula and short cuts as you know, solving questions for written exams is different.
All the best.

Hi,
Go to this link for fresh cut off list:
http://pict.edu/admissions/cut_off/

If you really want to prepare for JEE Mains then you are at the right place.
For physics you can study NCERT, HC Verma, for chemistry you can study Pradeep, NCERT and Arihant and for mathematics you can refer RD Sharma, NCERT, NCERT Exempler and book by ML Aggarwal.
There is a lot of competition in the outside world, so be prepared. If you want to get admission in a government college then you must have above 210 marks out of 360.

I am not discouraging you but I would suggest you to go for B.Sc and proceed ahead. If you accept my suggestion, then either go for B.Sc in Physics or B.Sc in Maths.
Feel free to ask more.
Good luck.