Can a child have a different blood group than both parents?

Yes,the child/children can have different blood Gr than their parents.

Parents AA child A or O

Parents BB child B or O

Parents AB and O child A or B can be possible.

No. The child will have the bood type of one of the parents. Also, a mother can carry a child that has a positive rh factor when she herself has a negaive rh factor.