Is it obligatory to wash the face up to the Adam's apple and to run wet fingers through the beard in Wudu, and how is the limit of the beard known?

The area below the chin is not part of the face that must be washed during ablution. However, it is recommended to run a handful of water through the beard. As for the "tahdheef" hair, the fatwa issued by our scholars is that it belongs to the head, and it is not obligatory to wash it with the face. If its meaning is not clear, then one should ask the people of knowledge about it.