In the living room, one of the outlets is just 3" right of the bottom windowsill and 6" down on the wall. I hope this helps!

The window isn't your issue; it is the plumbing which is. Don't you do it. Get an electrician. You need a GFI which protects you from shock anywhere in an area subject to moisture, like your bathroom.

In the bathroom outlet must be installed within 3' from the outside edge of each bathroom sink. The outlet must be located on a wall or partition adjacent to the sink counter surface, or on the side or face of the sink cabinet not more than 12" below the countertop. 1 receptacle outlet could be installed between two sinks to meet the requirement, but only in cases when there is a receptacle outlet within 3 ft of the outside edge of each basin, and of course all outlets must be GFI protected.

I don't think there is anything in the code that says the outlet cannot be near window's casing for as long the outlet is far enough so the outlet cover can be installed.