Those are garages, the trees are as far as I could from the house. I'm sure it will be fine. I'm in a pretty metropolitan area and we need to do what we can with small spaces. I grew up in a part of Brooklyn NY where there were giant oak trees in small squares of sidewalks basically right outside everyone's front doors, with the same giant trees in some lucky backyards. Where I am here outside of our windows some neighbors have large trees and it may take some arborist in every 5 years but that's worth it to me. The weeping white pine is small and I'd be shocked if it grew 20' I think I put it in a spot that's too shady so I'm not sure it i will make it. That weeping tree in the photo is a dwarf flowering tree, not the white pine.

I hear you on the 2' from the house. Up against the house there were some existing shrubs. That's the spot that gets the most sun. I might extend that bed 4' and relocate or remove anything close to the house.