Computers & IT (Non-Engg)

Although it's not mandatory, good maths background is helpful and required to become a good game programmer and designer.

Yes, of course. In fact, BCA+MCA degree is equivalent to B.Tech in CSE.

The main difference is that you will save 1-year. Go for the integrated course.

All the courses are good. Opt for the one that you love the most and are most passionate about and analyse the future work conditions, scope and growth prospects before taking admission.
You can also opt for psychometric test comprising of aptitude, personality, and career interests to clear this confusion.

Check out the list below ranking wise:
1 . Loyola College, Chennai
2. Christ University, Bangalore
3. The Oxford College of Science - [TOCS]
4. Fergusson College, Pune

I think you should opt for psychometric test comprising of aptitude, interest and personality to bring out your exact interest in computers.

Yes, you can Diana, 950 marks in the exam with cut-off of 141 is exceptional.

Yes you can, there is no age limit for pursuing Ph.D.