Degree

Both courses have it's own importance and have quite different content and objective. So, go through the content and decide which will be best for you.

You have to complete class 12th or it's equivalent to pursue a degree programme.

It is better to pass your class 12th with good grades and then focus for the IIT's and Iims that will be possible then only.

Hi,
You should complete your graduation first
This is the eligibility for AFCAT
Education: Graduation (min 3 years) in any discipline with min 60% marks and have passed Maths and Physics as subject at 10+2 level B.E/ B.Tech from a recognized University with min 60% marks. Age Limit : 20 to 24 years.

Check out IGNOU website. They might have good courses.

You cannot get a Bachelor's degree after class 10th. No recognized college in India provides such a programme.

You have to apply as foreign candidate in exam forms. Cost may be high for foreign nationals as compared to indian students. Mechanical engineering fee varies from college to college. If you are looking for government college, it may cost 20 k - 6 Lacs rupees. For private it may cost 5 - 10 Lacs. I will suggest you to give exams like JEE Mains for getting good government college.

Yes, you can apply as you are not having any Indian degree, so this will be easy for you to do it well.