I don’t know why not.

A shade closer in color to the light fixture would be less noticeable, but sometimes we have to work with what we have.

Yes you can mount it above the frame but it neededs then to stick out from the frame to operate . Why anything at all there since it does not seem to be a window open to anyone else. Is taht a public walkway on the far side of the pool?

I'd do an inside mount Duette-type shade in the same color as the trim/walls. It would only cover an inch or two at the top of the window when open and would blend in to make it barely noticeable.

Yes, all the way to the ceiling, since it is an outside mount.

Yes but you can't use the same shade you have. You will need to go larger so it is an outside mount. We usually come 5 down off ceiling an minimum 1 " -2" out on each side when doing this type of installation.

example

this is the INcorrect installation for an outside mount woven shade

This is the correct installation