NIT

You should pursue CSE from MNNIT. Just visit www.mnnit.ac.in and check for the placement.
You can also choose Warangal or Trichy.

The placements depend a lot on the economic condition of the country (e.g. recessions affect all). Unfortunately, Jalandhar has a slight locational disadvantage when compared to a place connected with an airport. A large number of recruiters seek easy travel options when it comes to going for campus placements. This trend is gradually changing for the better. The placement committee is working hard and recruitment scenario is becoming better each year. A large number of core companies are turning up.

It is next to impossible, even if you are from category. My suggestion to you is to apply in good local colleges in your state.

No, all the NITs don't follow the same syllabus, since they don't require so. All the NITs, Putting together 30 NITs are autonomous in nature. And so, they have complete independence in making any sorts of administrative changes or any syllabus they like. Much of the independence is vested in the hands of the Director, who can make any required changes in the system, If found to be necessary. This really helps in the rapid growth of the institute since most of its implementations are not directed by a Central governing body.

Go through the KCET college predictor link below for details:
https://www.shiksha.com/b-tech/resources/kcet-college-predictor.

Tough chance, but you can go through previous year cutoffs on josaa website, you might get chance in NIT Silchar or NIT Agartala.

Domicile certificate is for showing which state you belong i.e. where you reside. Lucknow and Allahabad is in the same state. So, it is not necessary to show. But, however it is dependent on college whether they ask for it or not. UP domicile certificate is needed for college outside of the state.

Yes, surely you are eligible, but you must have 60% in B.Sc in CS which you studied.

Dear,
Please refer NIT, Warangal's official website. They have provided opening and closing rank of each department as well as quota. By referring that you can expect your admission chances. Please don't consider that cutoff will be same for this year too. It changes every year but there is not much difference.

Both are best. If priority comes then it will be for NIT. But NSIT is also above as compared to some of the NITs. So you can go as per your preference.