What is the advantage and disadvantages of fixed beams?

There isn't really an advantage of having a fixed beam vs. a simply supported beam, it depends on what application the beam is for. If one of the design criteria of the beam is that it be able to deflect from one end to another then you are going to want to use a fixed beam. For example such applications could include a diving bored. A simply supported beam differs from a fixed beam because the beam is supported at both ends. Thus when a simply supported beam is loaded, the deflection will occur throughout the beam, since the ends are confined and will remain as they were. Furthermore on a fixed beam, (the end that is fixed) will have restrictive forces and moments keeping the end from moving.