Automobile Engineering

Mechanical engineering would be a better option.

Yes, you can get in automobile.

India has a very developed automobile industry and automobile ancillary industry. There are good opportunities for automobile engineering graduates in auto manufacturing and services sector. Nowadays, a lot of international automobile manufacturing companies outsource design and testing work to Indian companies. Also, a lot of MNCs have their design offices in India. In addition, IT companies hire automobile engineering graduates for thier engineering line of business. Therefore, automobile engineering graduates have good opportunities and scope for growth.

You may refer to the following link for a list of top automobile engineering colleges in the state of Tamil Nadu: https://www.shiksha.com/b-tech/ranking/top-automobile-engineering-colleges-in-tamil-nadu/51-2-123-0-0

With a number of Automobile companies setting up manufacturing facilities in India, Automobile engineers may do well. Life may be little tough for Aeronautical engineers (due to Flight Safety issues) but they do earn higher salaries. Select a branch as per your interest in that branch.

This is purely dependent on your interest and also the quality of the college you are studying.
B.Tech + MBA is a good option if you want to go for management jobs whereas if you want to go for pure technical job B.Tech + M.Tech.

You can do engineering in mechanical and automation after doing 12th in PCM.
There are more specializations and many will be added before you reach the 12th.