(1)t = 4, the distance between p and q is the shortest, because the quadrilateral APQO is a rectangle, and PQ=AO and PQ=AO are the shortest, which is certain.
(2) When t=7.2, the quadrilateral BCQP is a parallelogram.
(3) It is possible. When t=4/5, the quadrilateral BCQP is an isosceles trapezoid.