Hi Jean,
I also love to quilt with old shirts. They make the coziest quilts!
What I do with my shirts is "debone" them Bonnie Hunter style and then fold the large flat pieces and store them that way. It's fine to cut them into precut shapes then, but I don't. I never know what my pattern will call for so I don't precut.
Can't answer all your questions but I am really impressed by your organizational skills!