Engineering

Last year, the least marks required to get into mechanical were 101 in JEE Mains.
Hence, explore different opportunities.

Top 4:
RV, PES, BMS, MSR.

It's pretty similar to ECE. Mainly. Electronics.

Yes you can. At least for ECE.

You'll get it in the medium to lower ones such as MVJ, etc.

No. You need to complete MCA or M.Sc. before M.Tech.

Since you'll not get a government college with this rank, you can apply for a good private university such as LPU, KIIT, VIT, ICFAI, UPES, Amity, Sharda, Galgotia University, Manipal (recommended), Amrita.
Or get into one of the private colleges nearby you if you feel the placements are good.
Moreov

Yes, they will give preference to u

You can apply for counselling based on your 12th marks. Or else, apply for JoSAA counselling based on your JEE marks.

It totally depends on the college.
In government colleges, it ranges from 15k to 70k.
In private colleges, it ranges from 70k to 300k.
In NIT, it is up to 1,20,000 and in IIT, it is 2,00,000 (tution fee, excluding accommodation fee).