Could hemophilia occur due to a mutation?

Yes, a gene mutation. Hemophilia "a" is a hereditary bleeding disorder where there is a deficiency in clotting factor viii (factor viii is needed for blood clotting). It is inherited on the x-chromosome (sex-linked). Men only have 1 "x", so if their "x" is mutated, they will have the disease. Women have 2 "x's", so they can have 1 mutated "x" and 1 normal "x", and be a carrier of the disease, with mild or no symptoms.
Yes. The gene is actually a mutation, passed down from generation to generation. It can arise new, without either parent being affected in their own germline -- I'm told Queen Victoria was such a carrier.