Pretty impossible to put in a flanged window behind the stone. Some head flashing and coil work between the stone and the door/window will handle the water management. Long term, I would be more concerned about how they are sealing those cantilevered joists that are coming through the stone veneer. Way more leak potential in those locations than with the doors and windows.

Thank you! Can you link me to something that shows the head flashing and coil work you mentioned?

One project at some point will be to have that deck reviewed, I'm not a fan of the style the original owner chose either.

The way I have sealed block windows against stone or elsewhere where a nailing fin cannot be used is to over fill the gap with a high quality waterproof spray foam, (Dap, Loctite) After the foam has dried it can be cut flush with the exterior of the window or slightly behind, and then caulked over with high quality polyurethane sealant thoroughly, (Sika Flex) How tight the windows are to the stonework and the color of the sealant will determine if a trim piece of some kind needs to be installed over the polyurethane and then additionally caulked. Best of luck.

This would be ideal, but again you will have to have a quality installer that will know how to flash the windows. Being that far under the overhang, I am less worried about the windows as I am the deck.

https://www.copper.org/applications/architecture/arch_dhb/arch-details/flashings_copings/wall_flashing.html

Is that small section of wood siding going to be replaced?