Well - not a goose expert but I will tell you that geese are transient, so they may well have NOT been there when the building was there ;)

Geese need two things - somewhere to nest, and a food source. They are a big problem for large property owners and parklands, and yes, the poop is unpleasant. As for diseases, I have NO knowledge of any they carry that you may contract, and I work in healthcare ;) except for Bird flu and that's really, really rare ;), and mostly in captive animals i.e. chickens.

A dog won't work. The geese will beat it up unless it's a large dog ;) They can be quite aggressive, especially when nesting. My workplace actually closed an entrance as employees were being attacked by the nesting geese.

The ONLY thing I've seen work is a motion activated sprinkler - but they are expensive and only local to the area you place it in. Good luck!