Blood type and blood type b?

No - this is not possible. The child inherits one allele from each parent - and so at least one of the parents must have a B allele in order for the child to have blood type B. In this case the only...

A or B or ab blood

If B is homozygous (AB, BB): AB or B is possible.If B is heterozygous (AB, iB): A, B, or AB is possible.

No, the child can't inherit a B from people who are both A. The child can either have type A or O.

My elder sister have blood type AB, myself having blood type A and my younger brother having blood type O.