Are the reactions in galvanic cells always spontaneous? Why?
Yes. Galvanic cells are also called voltaic cells. The reaction that produces a voltage, and a current flow in an external circuit, is a spontaneous reaction, that is, it occurs with no outside intervention. A spontaneous reaction will have a negative value of Gibb's free energy, delta-G.
This video further explains why galvanic is spontaneous using electrical energy and free energy: