If you unscrew the clips you should be able to remove the screen frames. They are basically just a rectangle with a slot that the spline slips into (the spline is the rubber tubular gasket that holds the screen in place). Pull out the old spline with a pliers and the screen will just come right out. Take a piece of the old spline with you (the big box stores have this stuff) and match the diameter to some new spline material. There are a few sizes available so choose carefully for a snug fit in that slot. In the same aisle in the store, you will find a splining tool - a small roller at each end of a handle. One of the rollers has a convex edge, the other has a concave edge. Also in the same aisle, you will find fiberglass screening in rolls. Get a roll slightly wider than the screen frame that you are replacing. Then watch this video:
I did not have to cut glass to make repairs to my storm windows, but i did have to reseal them into their frames. I used clear silicone caulk. this was recommended to me by a window guy, who said that you can't even find the rubber gaskets that they used to use. Lay a thin bead into the frame and carefully set your glass or plexiglass into the frame. then lay another bead of silicone onto the top of the seam. I was a little sloppy here, but was able to trim away excess silicone after it dried.