Chemical Engineering

Hello, you can pursue your MS in Chemical Engineering itself or go for specializations like biomolecular engineering, petroleum engineering, plastic and dye technology etc. Chemical engineering is itself vast, you may go through program curricula in details of the universities and decide what would be best for you keeping your career interests into consideration.
Regards

Check the link and filter the colleges according to location :
https://engineering.shiksha.com/distance-learning-chemical-engineering-in-delhi-ncr-categorypage-2-58-630-0-0-10223-1-2-0-none-1-0

NIT-Trichy is one of the premiere institutes of India. If you ask specifically about chemical engineering, it is one of the best. About your second question, PSUs rarely come for campus placement. ONGC and BPCL have different off-campus recruitment policies and don't come to NITs or any other institute as well.There are some PSUs which come but the number is too less.

Depends on which institute you are looking to get admitted into. Old NITs and IITs have a decent cutoff. Exact figure varies form year to year and also your board percentile. Go through last year cutoffs to get an idea.

In India, the best is Institute of chemical technology,Mumbai. With you jee marks its really hard for you to get admission in NITs. If you are from a reserved category you might have a chance.

IIT Chennai
Anna University, Guindy, Chennai
SRM University, Chennai
Dr. M.G.R. Educational and Research Institute University, Maduravoyal, Chennai

go for job sites, consultants ,

Of course there is. There are many govt organisations that recruit chemical engineers like NTPC, NCPIL Reliance, ONGC etc. Although oil and gas sector is down right now, it is expected to be back to normal in the long run.