Yes. Vaccines have decreased illness rates dramatically, but there are some people who don't respond to vaccines and are still susceptible. This is one reason that a large percentage of the population needs to be immunized to make a dent in the transmission of a disease. Herd immunity protects if the immunizations aren't effective. (if others in the herd don't have mumps, you won't get mumps.).
Yes. It is possible to get mumps despite being vaccinated. This is because the antibodies that one develops from being vaccinated can diminish over time. Additionally, some infections can mutate thus causing the vaccine to be less effective. Generally, the disease one gets, despite being vaccinated, is less severe and shorter in length of infection.