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.

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.

EDIT: George Lowther correctly points out that this construction does not work for all sizes of billiard tables, so I'll be a bit more explicit about what I have in mind. Let the diameter of the balls be $d$ and let the table be of size $R\times r$ where $r<2d$. Put one corner of the table at $(0,0)$ with the sides of the table parallel to the coordinate axes and the side of length $R$ along the $y$-axis. Put the red ball at $(r/2, R/2)$ and the cue ball at, say, $(r/2, R/4)$. Let the wall be "all pocket" except for a point at $(r/2, R)$, which is made of "wall material".

Say a ball goes into the pocket if the entire ball crosses the boundary of the pocket. Now to sink the red ball it must move at least $r/2+d/2$ to the right or left (one cannot sink it along the $x$-axis, as it would have to pass through the cue ball to do so). But then by conservation of momentum, the cue would have to move at least $r/2+d/2$ in the opposite direction, which would be a scratch. (Indeed, the cue actually scratches before the red ball goes in, I believe).