All most all of the scrap quilts I have made do not have any stabilzer. There are some "patterns" that a stabilzer of some type is helpful. String quilt, crazy patch and a few others come to mind. The type that benifits the most from a stabilzer is irregular shapes, or pieces that are very small.
Muslin is a good foundation for these types, but other fabrics can be used as well. Old sheets, old pillow cases, ugly fabric , old shirts, interfacing , and some use ..used dryer sheets. If you are using a "ugly" fabric just make sure the fabric does not show through to the quilt fabrics being used. It may be that the wrong side of the fabric is more suitable.
Addind a border or sashing to each bock is a preference. Take a look at the "scappy quilt show" thread for pages and pages of insipration. Just use your search function at the top of the page, of the message board.