Chemical Engineering

In Haryana, the Polytechnic Diploma is equal to 12th and I feel the same is with you as well. If you are not interested in doing a B.Tech. You may go for B.Sc. In Chemical Engineering which shall take you to Post Graduation and then further Research area. Remember one thing that a Graduation should

Generally a score around 200 is good enough to get NITs. For Chemical Engineering also a score around 150-160 is good enough. Still, you can better check the college predictor link for the expected colleges list-
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

Yes, you can try to get admission for chemical engineering, but for that you have to qualify entrance exam if you want admission in a good college. If you don't want to give entrance exam, then you can try to get admission in any private college.

You might get admission in Chennai University, as you got poor marks in Maths, but you can get admission by getting highest marks in Chennai University entrance exam. You can try to get highest mark.

Yes, apply for good college if u get seat are good. You can get private college on the basis of 12th marks.

Yes, your marks are good enough to get admission here. You can try to get admission as you are eligible according to your marks. So, you may get admission.