You’ll be pleased to know the solution is very painless.
In the Brush palette, under Masking, you’ll find a button for “Backface Masking”. Make sure that’s enabled when you’re working on thin pieces and you’ll mostly affect just the surface you want and not what’s lying close underneath.
That should take care of most of your problems. That button needs to be pressed for each brush that you switch to, it’s not “live” across all brushes.
Also, for stuff like that piece of paper, you can create creased edges around it’s borders to help keep the edges in place when getting near them while sculpting. To do this you’ll have to mask and unmask areas to create polygroups, then hit “crease” in the geometry tab. This puts a crease down which really helps keep the edges intact when sculpting thin stuff like sheets of paper. In conjunction with Backface Masking you should have alot less problems.
(I almost always sculpt with Backface Masking on as default, imho it should be activated by default for most brushes and deactivated by the user, not the other way around how it is now.)