Briefly summarize how the pulleys worked with respect to changes in effort force and effort distance compared with resistance force and resistance distance. what are the advantages of using pulleys? what do you think would happen to the mechanical advantage if you added a third movable pulley?

It helps applying force in any direction. Pulley systems rely on the relationship between the load and the effort. It also increase the lifting distance. Useful for getting the drive action to happen in awkward places. The  bigger the mechanical advantage the lesser amount of force is needed to be exerted.