NIT

Hello,
I hope you are doing well. You have very good marks and rank in JEE Mains paper hence you are eligible to get the admission in NITs along with your favourite branch. Go for councelling, fill NITs with top ranking preference and get the best one along with your favourite branch.
All the best.

There is some chances of getting NITs and you can also get Government Colleges in your state.

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.