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!

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.

Yes, your rank is good enough to get a seat in Andhra university for geophysics. You can apply for admission. Good luck.

Hi,
Visit this link to check colleges based upon your rank:
https://www.shiksha.com/b-tech/resources/ap-eamcet-college-predictor