Distance

After diploma, u should take up regular btech. It will be much more beneficial fr u than any other distance course. If u want to join job, then u should opt fr btech (evening). All the best. Thank you.

In India, MBBS is only available in regular mode. Because One cannot acquire medical skills through distance learning mode. So Its not available in distance or part time mode.

If you are an experienced IT professional MCA by distance education will not be a handicap. But if you are a fresher then it may create few challenges and HR may try to hire you at lower salary in comparison to full time MCA candidates.

For distance education location of institute does not matter. Most of distance learning MBA are conducted on internet now. You can choose between various MBA based on your needs. I will recommend that you evaluate IGNOU for MBA. If you are an engineer BITS Pilani offers good options for MBA such as Consultancy Management, Manufacturing Management and Quality Management etc.

Yeah, you can work with them

You can opt for MDS. But distance learning mode is not available for MDS. You need to persue it as full time. Instead you can do some certificate courses.

Yes, there are institutes which provide distance learning and collaborative programs.
5 - 6 programs under BITS Pilani have been mentioned on their website too.
Even IIT Bombay has its Distance learning program, details of which are available on their website - http://www1.iitb.ac.in/~cep/about/index.html
Other local colleges also must be offering these courses.