Is it permissible to suffice with dipping the glans of the penis in the palm of the hand three times, or wiping it with a single tissue three consecutive times, or is it obligatory to use three separate tissues?

What you used to do by placing impurity in a small amount of water is not sufficient, because it contaminates it, and the impurity remains uncleansed. The correct method is to pour water over the impurity. As for using tissues for istinja' (cleansing after urinating or defecating), it is sufficient to wipe the urine with one tissue three times, covering the area of impurity, and it is not a condition to use three separate tissues. Many scholars consider it sufficient to cleanse thoroughly so that no trace of the impurity remains.