(1) The shortest chord passing through point P is perpendicular to the OP and divided vertically by the OP, so it can be made into a right triangle with a hypotenuse of 5 and a side of 4, and the solution is OP=3.

(2) Similarly, OQ=4, so PQ has two possibilities: 1 and 7.

(3) Equality. It is found that the product of the two parts of the chord passing through point P is equal.

(4) Let PC=x, then PD=25/3-x, x(25/3-x)= 16, 3x 2-25x+48 = 0, (3x- 16)(x-3)=0.