Have you adjusted the belt? It should be just tight enough that it doesn't slip. The little featherweights have tiny motors, so they don't like the extra strain of a tighter belt. It takes a little experimenting to get it right.
I haven't seen you mention a manual, you'll find tons of information in it, you can download one from here:
http://ismacs.net/free-sewing-machin...ls-list.html#S
That stuff where the cushion is, uh,.. well it IS the cushion. Sometimes they harden and crack, sometimes they turn to goo and look like someone schmushed bubblegum on it. Sometimes it hardens again after that. In the center of that mess, there will be a screw. You'll need to gently excavate that, and the rest of the cushion can be removed by chipping it off and out.