JEE Main Scores

Yes, you can get any of branches in any private college. You should either go for state counselling process or direct admission process.

Since the cutoff of CSE branch is more than other branches so to get it in NIT is not possible but you could take any other branches to get into NITs and if you'll work hard in first year then you'll definitely be upgraded to higher branches like CSE based on your performance.

You can get any private college. You should go for counselling or you should directly get the admission in private college as per the location you want.

You don't have a good score. If you want to know which colleges you can get then use Shiksha's college predictor and then compare your list of colleges in terms of placement and packages.

You may get till last round of counselling.

No buddy your rank will be invalid next year and on behalf of your next year's rank you will get admission in first year again.

Hello,
I hope you are doing well. Yes definitely you can definitely get any IIIT or NIT with your 5K ranking of JEE Mains. For your reference I am attaching a link where you can find the list of NIT and IIIT you will get based on your ranking:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7489993

In my suggestion if you are willing to do engineering and if you can drop on this year than do that but if you can't drop and want to pursue engineering this year then go for the all 7 rounds of counselling and of course there is a chance that you would get SASTRA.

You will get good NITs with decent branch. You should refer Shiksha's college predictor as well.

Please go to the college predictor link I am sharing here to know about the college you can get.
Link:https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.Good luck.