What are the differences between truss and beam elements? For example, how many degrees of freedom does a trussfirave?

The degrees correspond to axial displacement. There can be one, two, or three, depending on how the truss is oriented in three dimensions.

The degrees correspond to the relative positions of the nodes. There are three degrees for each node.

The degrees correspond to the relative positions of the ends of the truss. There are four degrees in all: two for each end.

The degrees correspond to axial and transverse displacements. Because every truss lies in a plane, there are two degrees of freedom.