Degree

You would have to clear your backlogs before you appear for any graduation programs.

If that is the case, then you would have to do the course as distance or correspondence. But, in a regular course that would not be possible.

Yes, this certificate will be useful in taking admission bin AUCET. You can use your A certificate.

All universities that are approved by UGC, have the authority to give out degrees to qualified students. These degrees are valid and recognized everywhere.

You can do B.Com, B.Sc or BCA. You can choose the course according to your interest.

Yes, distance degree is acceptable for MBA.

Yes, you can give SSC CGL and WBCS exam after completing your BCA from any institute. The eligibility for these exam is graduation only. Good luck.

No, it is not necessary at all. If you have basic understanding of the subjects, then scoring above 60% will be sufficient. You should focus on communication skills also to get placed in top companies through campus placement.
Yes, as you have scored first class in B.Com, so you can easily get placed in good companies.
Best of luck.