Masters

M.Sc/MA is related to your B.Sc/BA subjects. If you have mathematics in graduation then you can pursue M.Sc.

No, you cannot as you have done your BE in automobile engineering.

Masters of education is M.A in education like M.A in English and MA in political science. M.Ed is done after B.Ed.

Hi Pranay,
With a B-Tech qualification, I would suggest you to go for M.Tech Program and thereafter you can appear for NET Test conducted by UGC (Reference - https://www.eduncle.com/cbse-ugc-net-exam). This exam is the perfect gateway for those want to make an amazing career in the field of Research or Lecturership. After qualifying this exam you can have various career options with worthwhile salary packages.

No, in India only NID offers a UG course for exhibition design in India.

I would suggest you go for a Online Master Program Course. As it will help you to continue with your job & also help you in your salary hike.

Online Master programs are specifically designed Freshers as well as working professional who cannot take time off work to attend full-time Professional course. This program is particularly appealing to people who wish to advance their existing career. It can also be advantageous for people who have already developed a network of business relationships that can facilitate a change of careers.