I typically do not use stabilizer/interfacing when making T-shirt quilts - only if the T-shirt itself is very flimsy. I don't use sashing between the blocks but I do usually put a regular quilting cotton border on the quilt and use quilting cotton for the backing. I have made 6 or 7 of these now. All but one of them was twin size or larger. I machine quilt on my domestic sewing machine. Here is a link to one that I made.
http://www.quiltingboard.com/main-f1...ml#post4790296