What is the criterion for what prevents water from reaching the skin, and are substances such as blood, pus, discharge, beverages, and mucus, in addition to rubbed earwax and solidified fats on the skin, considered to prevent water from reaching it?

Ablution (Wudu') is not valid if there is something preventing water from reaching the skin on the ablutionary organs. The extent of what constitutes a barrier is a matter of scholarly disagreement. The criterion for what prevents water from reaching the skin is that which has thickness and prevents water from reaching it, such as congealed blood or other dense substances. As for light, liquid substances, they generally do not prevent it.