Re: Uneven floors and baseboards-foundation or sill issues?
It's not unusual to see the framing hanging from the central chimney mass, as the exterior foundation walls subside (usually on 200 year old houses with fieldstone foundations and gutter/drainage/sill issues) but the chimney stays at the same global height as built. It's not common to see this on a much younger house.
The beam looks like junk with the visible break between two timbers of the outside lamination. The only solution is to establish why the outer foundation/walls have dropped and stop it and then you could correct it by jacking and shimming the sill back up to the chimney height. This is best done when gutted, because the interior walls are going to be reformed to straight, not sagged.
The second floor being worse can be partially answered by the additional shrinkage of the second floor framing (as added to the shrinkage of the first floor deck; it's cumulative as you go up, the chimney stands pat)
Maybe it's as simple as your house being built with fresh-cut, green timber, of some species known for dramatic shrinkage upon drying. Fresh cut is only good for Xmas trees and flowers.
Remove not the ancient landmark, which your fathers have set.