Engineering

Yes. You should ignore the exam of the optional subject in PUBDET.

Yes, you can go for it.

You have some chance for getting government colleges. Go for counselling.

It is less likely to get one with your low rankings. You are only left to go with either private universities and colleges or a drop. Use this college predictor to get a better idea. https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=cconnect&utm_medium=CR_JEECP&utm_camp

You have lots of options. You can get into one of top - 6 NIT's. Though branch may be non - core. One of the suggestion be in MANIT or in MVNIT, or NIT-Nagpur. You are likely to get Chemical or IT in it. Check the list using college predictor:
https://www.shiksha.com/b-tech/resources/jee-mains-colleg

It's less likely to get one with your low rankings. You are only left to go with either private universities and colleges or a drop. Use this college predictor to get a better idea. https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=cconnect&utm_medium=CR_JEECP&utm_campa

Qualifying Exam and Marks: Candidates need to score a minimum of 50% aggregate marks in PCM taken together (40% in case of SC/ST candidates) in HSC or equivalent exam.

Though, hopes are there with you, as your category rank is supportive. Still, don't get dishearten, as you may be either get to sacrifice your branch or with college. You can also use college predictor. https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=cconnect&utm_medi

It is less likely to get a government college with these less number. Moreover, you can get one if any provision for state resident reservation is there or the college is not much crowded or applied by many of the students. Note: being a government college is not everything.