1. walking foot, has feed dogs on it so the layers of fabric move together, rather than the top sliding a bit. I alway use mine when attaching binding, or sewing seams that has batting in them. (like tote bags). You need one compatiable with your machine.
2. dropping feed dogs is used when free motion quilting.(fmq)The fabric does not move, you move it in any direction, circles, write your name.... They are lowered usually while using a darning foot, or free motion foot.
Hope that answers your questions. Someone else may post with more information.