Automobile Engineering

yes you are eligible

Use the links below for rank and college for MHT CET
https://www.shiksha.com/mhcet-college-predictor

you should go for automobile engineering. you should try for mechanical engineering too, if you get it definitely go for it otherwise automobile is OK for you. All the best

You can do MBA after MTech Automobile Engineering. However it may not add direct value addition to your basic education and high technical knowledge in automobile engineering. Once you do MBA you may become a generalist and may not even work in automobile industry. In case you want to work in automobile industry only, you may go for job now and do executive MBA or MBA by distance education after gaining few years of experience.

Anshul, you can join 2nd year of aeronautical engineering, as syllabus for 1st year of all the branches is same only.
For admission some colleges/ universities accept candidates through lateral entry scheme. You have to appear for Lateral Entry Engineering Test (LEET). You must have min.of 60% marks in diploma to appear for LEET.
If you have not given LEET too, then opt for good private universities like LPU, MIT, IIIT, DBU, etc. They offer world class environment to students along with good placements. Some even offer good scholarships to students. Check their websites.