I've read that change in entropy of a system is the same for a system in reversible and irreversible processes since it is a state function and does not depend on the pathway. Does this only apply to the system since I understand change in entropy of the universe is always positive for irreversible processes?
For an irreverislbe process with specified initial and final states of both the system and of the surroundings, calculating the change in entropy between the same two end states requires you to separate the system from the surroundings, and to devise a separate alternative reversible path for each to determine the integral of dq/T for each. This will give you the separate changes in entropy of the system, the surroundings, and the sum (i.e., the universe). So the reversible paths between the initial and final states will not typically bear much resemblance to the actual irreversible path that the combination of system and surroundings had suffered in the irreversible process.