Engineering

No, you cannot. You have to complete Diploma, and then can go for engineering by lateral scheme.

You can choose Stayabhama University, as the campus placements are more for Satyabhama University, but the fee is very high in Satyabhama University.
If you are not able to afford much expenses, then you can choose Andhra University.

Yes, it is compulsory to clear cutoff of every subject to clear JEE advance. You cannot qualify JEE advance with the help of one or two subjects. The cutoff of every subject is class 12-14 marks per subject, which can vary depending on the cutoff.

First, you should try to get college in the counselling, and also not only of JOSAA, but also of your state level counselling, which is conducted by department of technical education of your state to get any good government colleges of your state. If you won't get any good college, then you can take

When you take admission, then it will be included with the admission charge.

No there is a very less chance with his score.

No, you are not eligible for getting CSE in AU, but you have chances of getting some other lower groups.
So, please participate in the counselling conducted by AU from June 4th onwards based on your rank your date is given.

Your rank is too low to get NIT. You have to satisfy with any government college or private college in your state. Try to get government colleges for this you can wait for 2nd round of counselling, if you won't get in first round.

Comparing aeronautical and mechanical, mechanical seems to be better, the reason being that the mechanical engineers have vast options available in front of them because their degree is general in nature, and applicable to all types of industries that use machines. The scope of aeronautical engineer

For JEE Mains, it is enough to solve NCERT, MTG Maths and practice previous year papers. You can also practice from SL Loney (for trigonometry). For JEE Advanced more practice is required from slandered books.