Mechanical Engineering

Yes, electrical engineering is available at the Government College of Engineering but the course is B.Tech not BE.
Thank you.

Instead of doing Diploma in mechanical engineering, you should go for 12th class education and then take admission in mechanical engineering. The reason is that Government of Maharashtra is about to ban Diploma in mechanical branch. So, for making a career in the mechanical field, it will be beneficial for you to complete your class 12th.

Pillai is a good option. You can check out college and few other options.

Of course, you can do aeronautical engineering.
After completing any Diploma course in mechanical branch you can go directly to the 2nd second year after completing the Diploma.
I completed Diploma and the joined aeronautical engineering college.

Both the colleges are good and of government ownership.
So, it's up to you in which branch your interest lies.
Also, DTU has better standards than NIT, Delhi.

It's a bit difficult to comment as until we reach position before spot round as seat availability is also influenced by students who vacate seat at last moment to take admission in State Medical Colleges and till then it's difficult for AEC mechanical engineering.