Ah yes, Canon lenses are a lot cheaper it seems than Sony lenses. With the A7s ii you an use both APS-C and FF (full frame) lenses. With an APS-C lens you have to enable APS-C mode in the camera and it will result in a crop, and in my experience, a slightly noticeable drop in quality/sharpness especially in low light. That being said, APS-C lenses shouldn't be completely written off.
With regards to this lens, I check and it is a full frame lens so you are good to go!
With regards to your choice of adapter. I've personally used the Fotodoix adapter and it works fine. Sure you won't get the extra stops of brightness as you would with the Metabones speedbooster, but its a good low-cost alternative.
Image stabilization. This lens has IS which means that you can turn off IS in the camera and use the built in lens IS, OR you can manually set the zoom distance (mm) in the IS settings of the camera and turn off IS on the lens. The latter can be a pain because every time you adjust the zoom you have to change the mm setting in the camera, but you can always use a custom key to shortcut to it.