Is it a good choice to pursue MBA after completing B.Sc in chemistry?

Yes, you can do MBA after completing any UGC recognised degree, either Bachelor's or Master's. Since you are having a medical background, you can also choose MBA with specialisation in hospital management or something related to medical. Getting an instant job after graduation depends entirely on yo

Yes, you can do MBA after B.Sc. You need to appear for entrance exams like CAT, MAT, CMAT, SNAP, NMAT, etc.

Any graduation will make you eligible for MBA provided you clear aptitude tests such as CAT/CMAT/MAT etc. as applicable to your institute of study.