M.Des

Yes, you are eligible for both the courses. But, you will have to appear for entrance tests and get a good rank to get admission in the top colleges.

Yes, you can definitely choose M.Des. after doing B.Tech in mechanical engineering. You can either go for industrial or transportation design, both are equally good in terms of placement and are relevant according to your degree.
There are only two colleges that have M.Des. in transport design:
1. MITID, Pune
2. UPES, Dehradun
Top colleges for M.Des. in industrial design are:
1. Lady Sri Ram College, DU Delhi
2. NIT, Bhubaneshwar
3. NIFT's
4. IIT, Roorkie
5. UPES, Dehradun

You are running late for admissions right now. For admission in M.Des, you need to either give entrances like CEED, GATE, NID, NIFT entrance, NEED, etc. All of these exams are already over but don't lose hope as some private colleges are still open for admissions for vacant seats. You can apply for UPES – Dehradun, which has its next round of UPES-that test for M.Des on 19th August. Apart from UPES, you can also check MIT – Pune, if they have any next round of MIT-that test.

Professional of Transportation Design are in great demand in companies which manufacture automobiles, aircraft, watercraft, mass transit systems and two-wheeled vehicles etc. Moreover, placements are good in UPES. This year university has achieved 100% placements for design courses. And students of Transportation Design got an average package of around 7 lacs/anum and got placed in companies like General , Fortune , Elephant Design etc. So don't worry about the job opportunities and go for it if you've interest in this field .last date to apply for its UPES-that test is 9th July.you can apply for it.

Dear Avinash,
you will have to appear for entrance test to get into NID and secure good marks in it.

IIT or abroad both are equally good for master's because you will get a chance to be trained under world's best faculty. If you are looking for a global exposure, go ahead with universities abroad. Check this.
http://www.gsd.harvard.edu/#/academic-programs/master-in-design-studies/