1. This topic seems to be incomplete. There should be such a premise that CD and AB are parallel. From the diagram, they seem to be parallel (if they are not parallel, then the four points of PGHA will never form a parallelogram).

2. The topic is actually not difficult, just use the proportional relationship of parallel lines. The moving speed of line L in BC direction is sqrt(2), so the length of GC is sqrt(2)* t(sqrt means square root). Since HG is parallel to AB, GH/AB=GC/BC, and AB=4, BC=4*sqrt(2), GH=t can be obtained after being brought in.

3. Since GH is parallel to AB, if PAGH is to form a parallelogram, AP must be equal to GH. Because AP=AB-BP=4-3*t, we can get 4-3*t=t and t= 1.