Welcome to the board. Free motion quilting (FMQ) is machine quilting, as opposed to hand quilting, but possibly refers to just sewing in lines or 'in the ditch'.
A walking foot is for layers so they don't slip or move apart; a darning foot is used for FMQ and piecing is for sewing the blocks together.
Feed dogs up for walking foot and darning foot when down.
See above - best to use a walking foot for binding IMHO.
Happy quilting!