Andhra Pradesh

Go through the link.
https://www.shiksha.com/b-tech/resources/ap-eamcet-college-predictor
Here, you can search colleges according to your score.
You should choose as per your interest. AND I suggest you to take CSE if you have interest in it. Hope this helps you.

It is from June 8. On June 8, counselling would be done for ranks 1-8000 and then followed by consecutive days.

1. Dr. BR Ambedkar College of law, Pedda Waltair, Visakhapatnam
2. Siddhartha College of law, Vijayawada.
3. JKC College of law, Guntur.

Yes, you may have chance. Please visit mock counselling online tabs.

Yes, but make sure that by qualifying in AUEET you are going to dual degree course. Anyway, I think there is a provision for quitting the course after completing your 8th semester and to get a B.Tech certificate. But be sure about it. It's better to contact AU admissions desk for more information.

You can't get into mechanical in JNTU Kakinada with your EAMCET rank.

No, you cannot get into any university with this rank, but you have a great chance to get into good and top institutes in Andhra Pradesh.

Actually, you can't get into any government engineering college. But there are some colleges like AU and SVU which conduct AUEET and SVUEET entrance exams respectively and allow you to join in a dual degree courses based on the entrance exam score.