OK, I squat barefooted or on occasion with sandals. Get a much better feel and grip with the toes and whole foot it's self. Same reason I don't surf with shoes on, could not even come close to feel and control of the board. I've had PL'ing boots/shoes in the past, but to me always seemed so restricted when squatting. I'm flatfooted, pretty much born that way like so many of my family, so shoes never really helped me anyway. Best shoes I ever had was when I was playing college football. The trainers really paid attention to the right fit.
That tracking the knee/foot thing is very over rated, where is the logic in that I will never know. Knees not going over the toes...please! Let the knees, acting as hinges, follow their own natural path in squatting, DL's or any thing else. Take any foot position that may feel the best for and your body type. Everyone is different in this respect. Can't force a square peg in a round hole.
Knee pain sharp, moderate, aching, etc? Could be a knee cap thing, the start of arthritis, ligament/tendon, nerves inflamed, etc. A knee is a very complex unit and nothing really to be guessed at. Might want to have a checkup and see what people with more knowledge think.
Might try replacing squats with another leg exercise for awhile. Or start doing your squats once a week to see how the knee responds. Maybe even try adjusting the height of your bike seat, giving a shorter or longer leg stroke as you peddle. This can affect the knee's also. Good Luck.