Is one scoop of water sufficient for ensuring water covers the entire face during ablution, considering the presence of a beard, given that pouring water once stirs up misgivings about the water not reaching all parts of the limb and under the beard and arm hair, and there is a fear that this might be a mere wipe and not a wash?

The cause of the problem is waswasah (whisperings/obsessive thoughts). If the beard is thick, only the visible part needs to be washed, and takhleel (running fingers through it) is not obligatory. However, if it is thin and the skin underneath is visible, then water must reach the skin. This is done by pouring water over the face and rubbing it with both hands once, which is obligatory, and three times, which is preferable. The water naturally reaches the skin if the beard is thin. The scholars have explained the method of takhleel of the beard as taking a handful of water and placing it under the beard with interlocked fingers, or placing it from its sides and rubbing it, following the action of the Prophet (peace and blessings be upon him). One must limit oneself to this without excess and without giving in to waswasah.