Does wax adhering to the hand after ablution and prayer constitute a barrier that necessitates repeating the ablution and prayer? And what is the small amount of impurity that is excused, and how is custom determined in this regard?

The arrival of water to the skin is a condition for the validity of wudu (ablution). If there is a physical barrier that prevents water from reaching the skin, the purification becomes invalid, and this is agreed upon. So, if the wax was present before wudu and prevented water from reaching the skin, then wudu and prayer must be repeated. However, if it occurred after wudu, there is no need to repeat. Similarly, if you doubt its occurrence, the original presumption is that it occurred after wudu.