In the world of enlarging lenses, the 50mm focal length is designed to cover the standard 24x36 mm frame. For the most part, they are optimized for making 10x enlargements give or take a bit depending on manufacturer. Similarly 80mm enlarging lenses are designed to cover the 6x6 cm. film format, though the optimum magnification factor is a bit less. If you are getting prints with a sharp central portion degrading out towards the edges with the 50mm enlarging lens it's no surprise. No amount of stopping down or enlarger alignment is going to fix that. You need to use the lens designed to cover the film format you are using. You also need to insure that the light source evenly covers the 6x6 cm format as well. If it doesn't, then your prints will be lighter at the edges because of the light fall off.

Once you get that sorted out the most egregious of your problems will disappear. Check for alignment problems by using a grain focuser. If the center and edges are both in focus at your working aperture (two or three stops down from wide open,) you're all set. There's no need for alignment or for glass negative carriers. If not, start by aligning the enlarger; making sure that the baseboard, lens, and negative stages are all parallel. Glass negative carriers would be a last resort for me. Using one is not a substitute for the proper enlarging lens and light source; nor is it a cure for an improperly aligned enlarger.