Distance

Yes, you can do both the things simultaneously, there is no issue.

You should opt for MBA in regular mode. IT will help you to get good job opportunities and will also help you to groom your personality.

Through distance learning the best colleges for MBA would be Symbiosis Pune, IMT Ghaziabad, Sikkim Manipal University, IGNOU, ICFAI Business School Hyderabad, Annamalai University, Alaggapa University Tamil Nadu, Bharathidasan University. These are good universities for distance education. Some of these have online courses which you can pursue simultaneously with your job.

IGNOU, Sikkim Manipal University and LPU would be best for you according to my point of view.

Hello,
The fee structure of the course depends upon the subject and college in which you are getting admission. So, without choosing college it would be difficult to say. But, as per my view if you are seeking a good college then the fees would be in range of 25-35k.
Follow the link for some colleges providing distance Diploma:
https://engineering.shiksha.com/distance-diploma-in-maharashtra-categorypage-2-57-1-0-0-1-114-2-0-none-1-0

You can pursue CA or CMA course.

Yes, you can pursue both these courses simultaneously.

Following are the best institutes for distance learning programs:
1. IGNOU
2. Annamalai
3. Dr.B.R.Ambedkar Open University, Mumbai

You can pursue PG Diploma in sports psychology through distance in Mumbai University.