Ph.D

Hi,
Check the given link below:
You will get more information
https://www.shiksha.com/college/mit-Pune-mit-world-peace-university-kothrud-23583

1. Daulat Ram College
2. Jesus and Marry College
3. Keshav Mahavidyalaya
4. Mata Sundri College for Women
6. Indra Prastsha College For Women
7. Kamala Nehru College
8. Lady Sri Ram College for Women
9. Zakir Husain College.

Hello,
First of all, you need to select the college or University you want to go in. In Master's course they conduct an entrance while in some cases. The admission are direct, so you have to get prepared for both. It doesn't matter, if you come from good place or backward you have to work hard.
All the best and give a like.

Hi,
Here is the link which provide you information regarding Ph.D.
https://www.shiksha.com/engineering/articles/your-career-after-phd-in-engineering-blogId-4677

You can apply if your are in your final semester for Masters. Different colleges have different selection procedure for Ph.D. check for these admission requirements.

Yes, you can go ahead.

M.Phil gives you a glimpse of what research is, whereas, Ph.D is all about the research on a particular subject.

For a guaranteed job in India, most important is communication or you can say English and which can secure a successful career is, undoubtedly, maths.
Good wishes.

Not more than one year gap is tolerated anywhere in the industry. If you have 1 year gap then it is fine but 2 or more years are not valid and will lead to rejection.