AUCET

Yes, there are some chances to get a free seat in AUCET.

Yes, it's a good rank and there are high chances for you to get admission in AU.

No, you can't attend the counselling without a degree certificate.

Hi Pushpa, You rank is very good, you have a chance to get the seat in Andhra University but can't say correctly that you get a free seat or not, so, better you must check the updates on its official website. Here is the link below:
https://www.andhrauniversity.edu.in/
You can also email them for the enquiry. Hope this helps!

Kindly predict your college in this college predictor. JEE Main rank predictor is an online tool which predicts the candidates rank range and probable colleges based on the difficulty level of the examination, average marks scored in JEE Main and seats available in IITs, NITs, GFTIs, and other SFTIs. The rank predicted might not be accurate but it certainly does give an idea to the aspirant. Know your college admission chances based on your JEE Main Rank, Home State, Caste, Gender, etc. Here https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

There is good chance to get seat here. But, less chance for free seat.

According to your rank, there is a good chance to get this college.
Good luck.

Health certificate is needed for every institutes and for every counselling as it declares whether the student is fit to pursue the course or not. There includes small tests like diameters of the body, pressure, any deformity or disease and eye tests, quite simple. And, if you are making it for education purposes the designated doctor will know and make it according to the need of the institution or authority. Moreover you can submit it later after counselling. Good Luck.