Distance B.A

If you score more than 50% marks in BA degree by distance learning then you are eligible to seek admission in MBA (regular). You are advised to appear in MBA entrance examinations such as CAT, XAT, MAT, IIFT, SNAP, NMAT, etc. to seek admission in regular MBA degree course.

Yes, you can as it is allowed to pursue one distance & one regular course according to UGC.

As per the latest notification of UGC, you cannot pursue two degree courses simultaneously.
For more details, kindly refer to the link mentioned below:
http://www.ugc.ac.in/deb/notices/NOTIFICATION-PolicyonPursuingtwoormoreProgrammesSimultaneously.pdf

1. From Dr. BR Ambedkar Open University – Hyderabad, you can opt two subjects from arts stream like engineering, Hindi or Urdu literature, psychology, computer applications and the third subject from either commerce or science subjects like geology.
2. From Mumbai University, you can opt subjects like commerce (BA), psychology, philosophy, education etc.
3. From Annamalai University, you can do single majors in all arts and humanities subjects.
4. From Delhi University, you can do single major in BA honors degree in all humanities and arts subjects.

You may do the same from 2 different universities, but you have to check when the exams are held so that they don't clash.