Engineering Entrance Exam

You have try until 2nd Counselling, you will surely get the seat with this marks.

You'll get NIT but with lower rank and with branches such as metallurgy or mining. Kindly explore other options like B.Sc.

Yes, you are likely to get if not in Hyderabad then may be in IIIT-Allahabad.

Since there are only a few colleges which offer mechatronics engineering in India and one of them is IIT-D.

Sharpen your mind and intelligence. Don't focus on the trend listen to your needs. Start by taking small steps. Avoid any activity of getting depressed. Try thinking logically. Try solving problems rather than getting answers. Work hard for hours. And the smartest though should be " just focus of solving a 6 hours paper well rather than fighting with 12 Lacs smart peoples. " If you solve that 6 hours papers, you'll ultimately beat that crowd.
Best of luck.

You'll get a good branch in NIT, don't go for VIT. Though, getting into CSE of Manipal is a big chance. It is really great there. Moreover, other than CSE, you'll get other core branches easily with good NITs. Again, either get into Manipal or Amrita CSE or into other core into the good NITs.
Best of luck.

Yes, surely, you can appear for AAT if you qualify JEE Advanced cut-off.
All the best.

If you want to pursue engineering from premier engineering colleges like IITs and NITs. I would advice you to go for IIT preparation as it will also cover the portion of the studies covered at local coaching.
All the best.