How long does construction take for my buildings?

There is no precise answer.  The build time depends on several factors including how many peasants are set to build/repair and any researched upgrades from the university.

The buildings will not complete if you just sit around staring at the screen.  The best thing to do is to complete some quests and check back after you have done a few.  Keep in mind that not all buildings take the same amount of time to complete, so stock up on peasants and get to questing!