Design

Hi,
It is different for different institutes. Admission forms of institutes like NID, NIFT and PEARL will be out around November and December and will have their entrances around December & February.
For exact details of entrances, you will have to visit the website of the institutes you are interested in.

As mentioned in the above answer you can pursue M.Sc. You are already in the same stream.

There are many design courses. Be specific so that we can help you.

There is a lot of scope in web design and animation. But, you need to be creative and have good knowledge about computer for the same.

Yes, it is a right choice but there are other good institutes which you can check and join.

Yes, you can join if you are really interested in it.

An M.Des in automobile design graduate can become: Car manufacturers, two and three wheeler manufacturers, truck and heavy vehicle manufacturers or a special purpose vehicle manufacturers.
There is no good dedicated institute in Indore to pursue automobile design course, if you still wish to go for M.Des in automobile design, you can apply to one of these following colleges:
MITID, Pune
UPES, Dehradun

Yes, this is a good choice. NTTF is a good college and in future there is a good chance to get opportunity in your field.