M.Sc

If by fund, you mean scholarship there is a relaxation in Tuition fee, and other expenses by the IITs to its students who are toppers in their field of study.

That depends if your institute has a placement cell or not. You should check with the college where you would like to take admission in and if there are placements or not.

You will be able to pay off part of the tuition fee by doing a part time job. Placements depend on the college that you have taken admission in, most colleges have a placement cell, while others provide counselling and links to firms which hire off campus. Nowadays, there is nothing as an assured placement and it all depends on the will of the student to perform and work towards their goals.

The United States is the best when it comes to education in MS, and the most popular choice is Computer science nowadays, and I don't see this popularity index changing any time soon. However, the choice is entirely yours, there are many premier MS colleges in India as well offering relevant courses.

Please refer to the link provided below for a detailed list of entrance exams which are required to clear for admission into a course in MS in India:
https://www.shiksha.com/engineering/articles/m-tech-entrance-examinations-in-india-blogId-12539

Please refer to the link provided below for a list of colleges which offer admission into M.Sc (Chemistry) in Telangana:
https://www.shiksha.com/science/colleges/m-sc-chemistry-colleges-telangana

You can go either of the two. Generally University first offers Mphil and than PhD. M.Phil is "Master of Philosophy". It is an advanced post graduate research degree. You can contact your University from where you did M.Sc. They might be providing a research degree in your field. It can seek you a job in either government or a private college or University. Similarly PhD is done after M.Phil. A Doctor of Philosophy is the highest academic degree awarded by universities. In most countries PhDs are awarded for programs across the whole breadth of academic fields.