The way I understand it, the electron will always have some work function/energy required to free it because, e.g. in the case of conductors, a positive charge gets induced around the electron trying to pull it back when it tries to escape the surface. Meanwhile, for the case of insulators, the electrons are not free.
What do you mean by "bound electrons"?
The photoelectric effect in a metal ejects electrons from the conduction band. These electrons are not "bound" to any atom.
Maybe you could explain in more detail what do you mean with your question.