Can a player touch the ball or basket while the ball is ON or within the basket?
No.
Can a player touch the ball while the ball is within the imaginary cylinder which has the basket ring as it’s lower base?
No.
Is it legal for a player to touch the ball by reaching through the basket from below?
Not legal.
Can a player pull down the ring so that it contacts the ball before it returns to its original position?
No.