a. Good job! You correctly listed all the possible blood types in the children of a man with blood type O (ii) and a woman with blood type AB (IAIB). The possible blood types that the children could have are A (IAi), B (IBi), AB (IAIB), and O (ii). Additionally, each blood type can be either Rh-positive (+) or Rh-negative (-), which gives us the variations like A-, B+, etc.
b. Yes, you are correct. A woman with blood type AB can produce a child with blood type AB because she has both the A and B genes present (IA and IB). When she mates with a man who carries either an A or B gene, there is a chance that the child will inherit both the A and B genes, resulting in blood type AB.
As for having a child with blood type O, it is possible. Since the gene for blood type O (i) is recessive, a woman with blood type AB (IAIB) can pass along an i gene to her child. If the child's father is heterozygous for blood type (i.e., he carries the i gene), then there is a 50% chance that their child will have blood type O (ii).