Parents with type O and AB blood can have children with types A or B. A couple with types A and B can indeed have a child with type O blood, if both possess one recessive O allele. When a heterozygous type A individual mates with a homozygous type B, 50% of their offspring will have type AB blood.
Yes, a woman with type O blood and her husband with type AB blood can have children with the same blood types as their parents. A man with type B blood and a woman with type A blood can have a child with type O blood if they both carry the recessive O allele (genotype AO and BO respectively). Crossing a man that is heterozygous type A (IAi) with a woman that is homozygous type B (IBIB) will result in 50% of their children being type AB.
For the first question, because the woman has type O blood (ii), she can only pass on the i allele, and because her husband has type AB blood (IAIB), he can pass on either the IA or IB allele. This means their children can either be blood type A (IAi) or blood type B (IBi). For the second question, as type A and B parents could have the genotype AO and BO, their child can inherit the O allele from each parent (ii), resulting in type O blood. For the third question, a heterozygous type A man (IAi) can pass on either the IA or i allele, and a homozygous type B woman (IBIB) can only pass the IB allele, so 50% of their children will have the genotype IAIB, which is type AB blood.
It is very much possible for these parents to have offspring with the same or different blood types due to the nature of inheritance of the ABO blood group system which includes codominance and multiple alleles.