JEE Main

You cannot get admission in a government college. You should try to get admission in a private college.

If you belong to general or OBC category, you can get admission in a good government college. If you belong to SC or ST category, you can get admission in any of the NITs.

Its cut-off varies every year like it was 105 for JEE Mains (General category) in 2015 and was 100 this year for the same.

Yes, it is possible as there are many other entrance exams that you can give to get admission into petrochemical engineering. You can also get admission into it through JEE Mains.

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.