Automobile Engineering

In India 90% of colleges provide lateral entry for Diploma students. But, I checked their website, I didn't get anything about lateral entry. I would like to suggest you to contact them directly and ask about it. Following link will direct you to the contact and course details.
https://www.shiksha.com/b-tech/course/b-e-in-automobile-engineering-psg-college-of-technology-coimbatore-114882

There are many good colleges for Automobile Engineering in India. It totally depends on your location and your eligibility about the college which is suitable for you. I would like to suggest you to visit Shiksha.com for best colleges in your area.

There are 12 colleges in Telangana, which provide Automobile Engineering course. Following is the link which will direct you where you can find details of the colleges. You can find good colleges in your location according to your eligibility. https://www.shiksha.com/search/?q=Automobile+Engineering&sp[]=45&sa=^413^0^0^45^0^0^0^0^0^0^0^0^0^sp:45&rf=searchwidget&st[]=413&pn=1&sscs=1&tk=Aut&ii=1&s[]=2&tscs=1.

First of all, congratulations for getting placed in TVS motors. If you want to complete your UG course while working, you can do part time UG course. You can find many part time UG course providing colleges in your location. You should visit Shiksha.com for required details.

In India, about 90% of colleges provide lateral entry for Diploma students. I checked SRM College's official website, but I couldn't find any details about lateral entry. And, if there is lateral entry, you have to write an entrance test for it. I would like to suggest you that you directly contact them and ask about lateral entry. Following link will direct you where you can get some information. https://www.shiksha.com/b-tech/course/b-tech-in-automobile-engineering-srm-institute-of-science-and-technology-chennai-kattankulathur-campus-kattankulathur-242610.

I found that Aurora Institute is good for Automobile Engineering with average fees and good placement. If you are willing to get admitted there, you should write an exam called TS EAMCET (Telangana state Engineering Agriculture and Medical entrance exam). The dates of this exam are coming near in the first week of May. So, I would suggest if you are willing to do engineering here, you should apply and prepare for the entrance exam. Details of the college and admission details are in the link below.
https://www.shiksha.com/b-tech/course/b-tech-in-automobile-engineering-aurora-group-of-institutions-aurora-hyderabad-chikkadpally-248176

Yes, you can do part time Masters in Automobile Engineering course. I have visited their page and I found that they provide Part time course. Following is the link if you want to check by yourself and contact them for more details. http://www.msruas.ac.in/fet_pg/pg_programmes.

The percentage required for students from other state is same as the students from Tamil Nadu. But I could't find what is the exact percentage required. I would suggest you to directly contact them and ask the cut-off. Following is the link with contact details of MIT. http://www.mitindia.edu/en/contact-us.

I searched in the official website of MHSSCE, but I didn't find anything about Diploma in Automobile Engineering. Instead, I got information about B.Tech in Automobile Engineering. I would like to suggest you that you directly contact them, following link will direct you to their contact details.
http://www.mhssce.ac.in/CNT/LCMP.php

Yes, of course you can apply. More than India, there is high requirement of Automobile Engineers abroad. I would like to suggest you that you can apply for jobs in Dubai or Germany. Because these two are the places where there are high requirement of Engineers.