for your first question- the fusable-pressing cloth-and your iron---fabric will stick to the fusable---and make a mess- parchement paper- or a teflon pressing sheet- or even release paper from used fusable works well to protect your iron-and pressing surface.
for your second question- yes an old towel is fine- to use for your damp pressing cloth.
as for the clothes clinging well- i would think with the fleece they would---if that is the back- if both sides of the fleece are covered with fabric it would depend on the fabric- flannel clings well- regular cottons-not so much - if you are only fusing one side of the fleece-the fleece will also cling well