I think that the answer to Q1 is "no" if we allow the problem to be generalized sufficiently, (e.g. we allow large pockets, and small balls) even if no balls are touching in the initial configuration. Consider the following "billiard table": the entire rectangular wall consists of "pocket" except for a single point at the midpoint of one of the walls. Now place a single red ball in the very center of the square, and place the cue ball on the line connecting the ball and the "wall point," on the opposite side of the ball from the "wall point." Then we have no opportunity to ricochet, as red ball blocks the cue's path to the "wall point." So we must hit the red ball immediately--but it is easy to see that for balls of small diameter, whatever shot we attempt will result in a scratch. Now, it seems to me that the condition of "scratching" is an open condition in the configuration space of the problem (e.g. parametrize by wall endpoints, ball positions, felt damping coefficient, shot angle, etc.--here I assume walls are possibly empty closed intervals and balls are closed balls) so this counterexample gives infinitely many (slightly less trivial) counterexamples.