Insulate the cavity between the window and the masonry!

You first build up the wall and then install the windows. Cutting your stones is not a problem at all, or are you laying the bricks yourselves and don't have a saw? Styrodur can be used, but it has to be properly glued and then a mesh should be spackled over the joints, but it's not optimal.

Yes, normally you build up the wall and prepare the [laibungen] with mortar for the RAL installation. That means you fill the holes and create a smooth surface. I also don't understand why there are gaps there with you.