Which of the following actions is permitted on the putting green?

Marking, lifting, cleaning, and replacing the ball is a permitted action on the putting green according to the Rules of Golf. This procedure allows players to ensure their ball is clean and free of any debris that could affect its performance on the green. When a player marks their ball, they are indicating its position, and lifting the ball for cleaning is essential to maintain fairness and consistency in play. The replacement of the ball must be done in accordance with the rules, whereby it is replaced on its original spot.

Changing the position of the hole is not permitted as it is typically the responsibility of course officials and should remain consistent throughout play for all competitors.

Removing other players' balls is also not allowed unless they are in the way of your shot, and even then, the procedure requires approval from the owner of the ball or following specific rules to ensure fairness.

Touching the flagstick while putting may be allowed in some contexts, but in competitive play, it is generally advised to avoid interference with the flag during a putt, as the ball could potentially hit the flagstick and change its trajectory, impacting the fairness of the outcome.