Full Time

No, it's not possible. You can do MBA either in distance or regular mode. One famous university which offers distance MBA is IGNOU. Kindly go through the website for better understanding.

It's nothing like that. Both courses are equally good. Regular MBA is mostly for freshers and people with 1-2 years' of work experience. Executive MBA is only for working professionals.
https://www.shiksha.com/business-management-studies/ranking/top-executive-mba-colleges-in-india/18-2-0-0-0
Please click on the above link to get a list of good executive MBA colleges in India. Choose the best college for you by comparing the colleges with:
https://www.shiksha.com/resources/college-comparison

Yes, it is possible you may apply to TISS (alone MPhil is not available you have to do integrated M Phil and PhD) and you may search other institutes too.
Please also note that institutes may ask UGC DEB approval and AICTE approval to your distance MBA program.

Yes. Migration from SOL to regular colleges allowed with following conditions:
1. You should not have any backlong I.e. you must have cleared all the subjects
2. The respective college should have seat and you must get the percentage in BA first year to compete with other students in merit.
3. You need to submit NOC from SOL.