This is just to address the "hook" mentioned earlier.
My cue hooks to the left 6 inches past the CB. I have found the cause to be that during my extended follow through with my elbow drop, at the 6 inch mark my closed bridge forces the cue into the cloth almost like applying a brake. To avoid digging into the cloth my wrist and elbow relax and swing out wide. From doing this drill thousands of times the marks are wore into the cloth. The line is clear -straight through the cue and six inches past, then the hook left. In a video it can be seen that I don't do this on center ball or high hits so I'm pretty sure it's due to the reason I mentioned. Maybe it's the same cause of yours?
I don't think it's from friction of the cloth. Most likely is that you are not correctly lined up to start with, slightly steer the cue, then when you do relax the cue starts going down it's actual natural path that your arm and wrist are lined up to.
Fixed this with a student today just by having the person relax the grip, make sure that when their arm just swung naturally it was on the shot line, and point the thumb down.
Yes, I still have a few flaws to work out in my own stroke. :smile: