Can I pursue MBA after completing BA?

Yes, you can do MBA. Anyone can do it, if one has completed graduation with at least 50%.

Yes, but you won't be eligible for some important exams like CAT, NMAT or SNAP. You can only give XAT and MAT. You can check the eligibility criteria of the various exams.

The eligibility criteria is 50% aggregate for open and 45% for other categories. Even, if you get into any college, placements will be an issue because companies also have the same eligibility of 50% aggregate in graduation.