A steel ruler, a couple of utility knifes and a pack of blades is one of the best investments you can make.
You can pull up a piece if the rubber cement is only applied to one surface and put down while wet. If there is dried rubber cement on each surface (back of print and carrier) then it is as good as stuck.
As for final positioning and adhesion: if the pieces are square, you can put a clean blank sheet of paper between the print you are adhering and the carrier sheet while you align the piece and then slowly pulling the clean sheet out while you press it down to make it stick. Practice a few first and you will get the hang of it pretty quick.
Hope that helps.