Engineering Scope

Both the areas are good and have an immense scope. Material Science which is an interdisciplinary degree is offered only by a few top universities as Master's degree. Materials engineering graduates have jobs in materials-based industries such as vehicle construction and mechanical engineering, chemical industry, information and communication technologies, energy supply, electrical engineering/electronics and metal production and processing. Germany is known for mechanics and automobiles and this industry is the country's driving force. Check the Make it in Germany website for more career information.

Petroleum Engineering graduates are in good demand with Oil and Gas Public sector units in India.

There is not much, but if you pursue from a good institution German companies will surely recruit you.

BE offers more salary and has better job opportunity than BHM. After BHM, starting salary is less as compared to BE and also after MHM, you will get salary which will be equivalent to BE plus 2 years of experience. Growth in terms of salary and career is good in case of BE and a bit slower in hotel industry.

Yes. Infrastructure is an emerging line.
You may easily get a job as field officer or site inspector.
If you are unable to get a job than contact your local contractor for job.

Mechatronics is a good field. Your objective is also very good. But what you said here is not enough to get a job in NASA. You have to do something extraordinary, something big like Ph.D to get the attention of NASA, and after that only they will call you.
I suggest that NASA is very good but nowadays, ISRO is making good progress in aerospace research, so as an Indian, you should try for ISRO first.

Kindly specify the level of education you wish to pursue. Every level has a different approach.