Yes the fleece will work on place-mats and small wall hangings. I fuse it to the backing fabric and then quilt with the top layer. The fusing helps keeps all the layers together.
Do you have local guild or quilt shop that you can call to arrange pick-up. Perhaps even a local charity or hospital could arrange pick up directly from you. Reach out and make a few phone call to inquire of needs.
Best wishes with your fabrics! It's always fun to see the end results!