Leaning the ladder against the gutter
If the gutters are safe to lean on, and if there are no potential problems with denting them, then that is the way to do it.
The ladder will be stable and you will be in a better position for cleaning the gutters than if you were on a ladder leaning on the walls.
Some gutters are actually strong enough that you can lean a ladder against them without any issues; not even a risk of aesthetic dents. I talked to a guy who hand crafted and installed gutters and he said that for some buildings they install extra strong gutters because they know that ladders will be leaned against them or they know that kids will be hanging in them.
Don't lean the stabilizer on the side of the gutter since that involves a risk of the stabilizer arms suddenly slipping below or above the gutter. Instead, do not use the stabilizer or if using the stabilizer place it above the gutter so that the ladder itself is leaning on the gutter.
Leaning a two arm stabiliser against the window area, not a good idea in your case
The stabilizers that I know of all have two "arms". Even if you place the ladder correctly and the spacing between the arms will rest against the framing, then that is not really good enough in my opinion. There is a risk that something gives in and the top of the ladder moves a bit to the side, in which case one of the arms will suddenly lean against the glass.
Leaning a stabilizer against the roof
From googling it seems that many ladder stabilizers are built to be used like that as well.
Avoiding using a ladder
This is what I would do if I had a house like that. You can get remote controlled gutter cleaning robots, eg iRobot Looj or you can get accessories for a power washer that lets you clean the gutters while standing on the ground eg Gutter Ball.