yes all spontaneous reactions do increase entropt of the universe.
D=delta
DG=DH-TDS
this equations is used to determine spontaniety.
DH= - and DS= + then reaction is spontaneous at all temps.
DH=+ and DS= - then reaction is not spontaneous.
DH= + and DS= + then reaction is spontaneous only at high temps.
DH= - and DS= + then reaction is spontaneous at low temps.
you can apply the equation above if they give you a problem dealing with any of those variables. Im pretty sure im right, but someone correct me if I said something wrong (its been a while).