Degree

Definitely you will get M.Sc. Physics. The general eligibility criteria of most of the colleges is given below. Eligibility criteria : The candidate must have passed 10+2 or equivalent examination by a recognised board and B.Sc. Physics with 50% or above marks in aggregate. The candidate must have passed B.Sc. (General/Programme/B.Sc. (Pass) B.Sc. (H) Electronic, B.A. /B.Sc. (H) Instrumentation B.A. / B.Sc. (H) Electronics with 50% or above marks in aggregate. Further candidates appearing in their last semester of papers can also apply. Hence if you are writing the final exam of Bachelor degree than you are eligible for M.Sc. Physics.

Hi
I think final year/semester candidates can give the exam. You will have to check the notification to know about eligibility criteria. https://www.shiksha.com/mba/tancet-exam-dates.

Hi
Don't go for Masters through distance mode. It will not having much value in future. For information about validity of degree check the accreditation of university.

You can ask to college department. To get admission to BCA BBA & B.Com students need to follow the following criteria respectively:
Students who have passed the 10+2 or equivalent (with Physics, Mathematics and Chemistry) are eligible to apply for a Bachelor of Computer Applications. Students who have passed the 10+2 or equivalent examination from any recognised board or school are eligible to apply for a Bachelor of Business Administration. Students who have passed the 10+2 or equivalent examination from any recognised board or school can apply to Bachelor of Commerce.

The MCC Bangalore offers Honours degree in B.A. Communication studies and B.Com only. Hence Honours degree in Economics is not available at Mount Carmel College Bangalore.

Yes, after completion of your degree, you can do that as well. No need to worry.