I've just built my very first house (Heartfire DLC). I went downstairs and I had to fight 5 skeevers. Will they respawn? Can bandits vandalise my house/stables/etc.? Can a follower stay there forever and take care of those circumstances?
I never had mobs spawn in my house, but I regularly had thieves, giants and other nuisances right outside of my home.
And neither my housecarl nor anyone else took care of them. My assumption is that they do not spawn unless you are there.
The skeevers are an exception to appear as a house pest in the cellar. You wive might alert you that she heard something. You can also keep one of them as a pet if you have kids.