HI and welcome to the board. Usually wool precuts are already felted and they are used for wool applique. Felting process preshrinks so they should be machine washable with no issues. The beauty of felted wool applique is felted wool doesn't fray so it is all raw edge with usually a blanket stitch done to adhere the shape to your background. Traditionally wool for this purpose is cut in sizes 8" x 14" and sold in bundles but sizes do vary from supplier to supplier.
You can freely mix wool with cottons. Many people use wool as the applique and a standard quilting cotton as the background.
Here is a website to give you ideas of what can be done with felted wool.
https://www.primitivegatherings.us/