Can I use cookie cutter shapes in a frying pan?
In general places that do this with pancakes do not cut-out, but indeed use a mold or the like.  The scrambled eggs would likely look fine "cut", but part of a pancake is the edge, even if it is modified by touching the edge of the mold.

So long as the mold is metal, your dollar-store purchases should be fine.

You will likely need to oil/butter them in some way so that the product - batter or egg - does not stick to the metal itself.

I have myself used clean old tuna tins to make round "self-contained" fried eggs for a home version of a McMuffin.