Yes. Blood types are inherited from both parents.
Complicated genetics. The genetics of blood type are fairly complex. It is indeed possible for a child to have a blood type different from either parent. There are, however, certain parent-child combinations of blood types that cannot occur together. Here's a website that explains it pretty well. http://learn.genetics.utah.edu/content/begin/traits/blood/.
Yes . The genetic transmission of blood type depends on the fact that each parent has two genes for blood type. That is to say a person with blood type a could have genes of aa or ao. If a parent with blood type ao (one version of a) has a child with a parent with blood type bo (one version of b) , the child could still be blood type o.