Is what the questioner did—cleansing with tissues by wiping the penis, then folding the tissue and wiping with the clean side, and repeating this several times—excusable, given his ignorance of the ruling regarding urine exceeding the area of purification? And what is the ruling on his prayers?

The best method for istinja' (cleaning oneself after relieving oneself) is to combine wiping with tissues and washing with water. If one limits it to wiping with tissues, then wiping three times is sufficient if it covers the entire area. However, many scholars do not stipulate a specific number, rather, for them, thorough cleansing (al-inqa') is enough. Wiping with tissues is sufficient even if urine reaches the tip of the glans (al-hashafah), as long as it does not go beyond it. Assuming your istinja' was insufficient and you prayed out of ignorance, your prayer is valid and you do not need to repeat it.