IGNOU - Indira Gandhi National Open University

Yes, you definitely can.

No, you cannot get direct admission. Open MAT is compulsory to beat to gain admission in IGNOU for MBA.

OPENMAT exam is conducted twice a year for MBA in IGNOU, once in July and then in December. Check this link for official details.
http://ignou.ac.in/ignou/studentzone/adminssionanouncement/Management

Hi Rohit,
Regarding correspondence education. There are many universities like:
However, IGNOU has the toughest evaluation process so, one would have to work hard as IGNOU doesn't provide the best quality teaching. Overall, the result would greatly depend if you can do self-study. However since all these facts lead us to work hard by ourselves and, I believe IGNOU is a better institution ( than SOL DU, as you might not get much support from DU ).

Yes, you are eligible:
http://www.ignou.ac.in/ignou/aboutignou/school/soe/programmes/detail/72/2
Follow the link to know more or reach out to your the nearest IGNOU center to know more.

Yes, you can. Check the link for more information:
http://www.ignou.ac.in/ignou/aboutignou/school/soe/programmes/detail/72/2

Yes, you are eligible. To take admission in M.Com or PG Diploma, you must be graduate from any recognised university. You are an existing student of IGNOU so you need to use your PRN number and apply on the IGNOU website.

Hey,
No when you taken admission for one particular study center you must actually complete your course right there as you have registered yourself in that particular center for BA degree. You might still request them to change your study center but it's not possible to study in other college.
Thank you.
For any more assistance, please feel to leave a comment here.

Yes, you can complete the course. IGNOU course is an open course, and can be done from home. So, I think you can join IGNOU for pursuing B.Sc.

Do not drop now after 3 years. It would take 3 more years to complete graduation, no matter what and also nearly same amount of fee. Just endure for 1 more year, then at least you will have a graduation degree in a year rather than 3 years. Also, talk to your friends and parents before making decision. They will suggest you same.