Inflow roll (transverse flow) and flapback are both examples of the rotor disc flapping to equality - with inflow roll there is a difference in inflow angles and thus induced flow between the front and rear of the disc - with flapback there is a difference in Vsquared and thus lift between advancing and retreating blades.
The flapping (and especially the damping that reduces the flapping) is due to the aerodynamic forces and not to gyroscopic precession - this is proved by the fact that phase lag changes from 90 degrees with density altitude and rotor head design - a gyroscope wouldn't experience these changes but that is what is taught by many schools because it is sometimes easier to understand.
Translational lift is due to a change in the inflow angle and thus induced flow across the whole disc as a result of moving - forward to keep it simple but in any direction since the disc doesn't know or care where the air is coming from.