Using a surface force balance with high sensitivity in measuring shear forces we investigated the mechanical properties of thin layers of cyclohexane and octamethylcyclotetrasiloxane (OMCTS) in the gap between two smooth solid surfaces at discrete thicknesses n=6-3 molecular layers. At these layer thicknesses the films have undergone solidification due to their confinement (see preceding paper) and are capable of sustaining a finite yield stress upon being sheared. The sliding of the confining surfaces at mean velocity nu(s) across the films is characterized by a shear or frictional force F-s which varies with a characteristic stick-slip pattern. We investigate comprehensively the dependence of F-s on n, nu(s), and on the applied normal forces F across the films. We find that transitions in film thickness from n-->(n-1), with a consequent increase in F-s, may occur spontaneously during sliding with no change in F, corresponding to a multivalued friction force between the surfaces for a given load. The critical yield stress S for sliding at a given film thickness n increases monotonically with applied normal pressure P as S = S-0 + CP where S-0 is a constant of order 10(5) Pa (depending on n) and C is roughly constant and of order 1. A simple model for friction across such films which can account semiquantitatively for this behavior is introduced, based on a shear-melting mechanism using the Lindemann criterion. We find that the characteristic stick-slip behavior persists over the range of film thicknesses and the entire (large) range of mean shear velocities studied, and that over most of this range the mean shear forces are independent of nu(s).