NIT

You will get your preferred branch in some NIT and core branches in Good NIT. Even you have a chance of getting get BIT Mesra (not CSE).
I hope it helps.

You can check the prevoius year's cut-offs of your dream institute on the website of that college. For NITs and IITs, you should visit: JOSAA.NIC.IN.

IT all depends upon the rank of the JEE MAIN paper. You can check the previous year's cut-offs of various institutions on JOSAA's website.

There is no harm in taking a drop for a year for preparation. But remember one thing do only if you have dedication and belief. If you can work hard for a year and maintain distance from all the distractions. I have seen students studying for 2 year for preparation, but they even don't clear the cut off. Also I have seen students taking a year drop and working so hard that within a year of studies they crack the exam with good marks. It depends on you, if you can focus on studies only, then take a drop, become a NITian. Good Luck. Hope it helps.

No, you are eligible to get seats in NITs. But, you can get any other government colleges. You can apply once the counselling lines are open.

CSE is good branch. VIT also a good college but if you get seat in top nits as NIT Warangal, etc. Then, you should go for NIT or it depends on your interest also you want to choose CSE or chemical engineering.
Good luck.

In NITs, college placements are good. Yet, in the basis of placement, only I suggest CSE. But, I think it depends upon your own interest. Every branch is good.
All the best.

No chance of getting NIT. But, there are also other good colleges
Try in them.
All the best :)

Yes, you are likely to get a seat in NIT, so don't worry about it.
You may not make up till NIT-K, NIT-W, NIT-T, but you can get NIT Rourkela, NIT Silchar and most of the IIITs.
If you go for top NITs, you may not get the desired branch but you can get a core branch in NIT Silchar.
In NIT Rourkela, you can get a dual degree in civil. Best of luck.

If you want to get IIT/NIT in your native, you need to score high in IIT-Mains/Advanced. To score high in IIT entrance exam you need to put a dedicated effort. Practice a lot, keep make note of tips and tricks. Try to solve as many problems as possible. Take tests to evaluate yourself. Best of Luck!