Much of what buildings do can be seen from looking at the game files in gnome, particularly crusaders_build_prod.

The files seem to claim the university has no function, save for being a prerequistite for other buildings, and as a GA goal.

The various churches/mosques claim to have a morale upgrading effect. +1/+2/+3 for increasing levels, and they also apparently spread your faith.

An inn attracts mercs, but larger castles drive them away, as will a constable's palace or a marshal's palace.