NIT

Yes, sure. You can check the college list for which you can apply on the basis of your rank:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Your rank is a little bit high for getting NITs or IIITs. But you can check on the college predictor link:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Hello, I hope you are doing well. You can check the list of colleges including NITs and IIITs that you can get according to your marks and rank in Andhra Pradesh. Use Shiksha JEE college predictor:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7489993.

Hello,
Hope you are doing well. Yes, definitely you will get IIIT or NIT with this rank in JEE Mains along with your branch. For your reference, I am attaching a link for you so that you will get the tentative college you will get based on your marks.
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7489993.

For NITK, please compare with the cut-offs of the last year.
https://www.shiksha.com/college/national-institute-of-technology-surathkal-mangalore-24187/admission#admission

If you are eligible to get a seat in Electronics and Communications, then I would suggest you take it over Electrical and Electronics in NITK. As EC is a better branch in terms of faculty and placements, then EEE in NITK.

Hello,
Hope you are doing well. Yes, definitely you will get NITs on the basis of your rank and marks in JEE Mains. Go for counselling, and get the best NIT with your rank. All the best.

Please compare with the cut-offs of the last year for NITK.
https://www.shiksha.com/college/national-institute-of-technology-surathkal-mangalore-24187/admission#admission

I think it is very difficult. But you may try some other colleges which give admission even if you are qualified in JEE Mains. I don't know the colleges exactly which provide such admission. In addition to that, it is also advisable to go for JoSAA options entry as many seats are being vacant in the past few years.

I think it's difficult for you to get MNNIT CSE if you belong to general category. According to me, both are good, but in MNNIT, you can opt for IT and after 1st year if your CPI is good (above 8.5) then you can change your branch to CSE.