How did the Prophet (peace be upon him) and his Companions wash their faces and the roots of their hair with a single scoop [of water], even though washing them takes time and effort? Is it obligatory to wash the earlobes? And what is the ruling for making water reach under thick hair of the beard?

It is recommended to abandon waswasah (obsessive whispering/doubts) and turn away from it. The obligation in washing the limbs for wudu (ablution) is only once, and anything more than that is sunnah (recommended). Washing the entire face once is sufficient, and there is no difficulty in that except for someone afflicted with waswasah. As for the hair roots (manābit ash-sha'r), what is meant are the roots of normal head hair. So, a bald person suffices with washing his forehead. The earlobe is not obligatory to wash in wudu; rather, it is sunnah to wipe it according to the majority of scholars. For a thin beard, it is obligatory to make the water reach the skin beneath it. As for a thick beard, washing its surface is sufficient, and it is mustahabb (recommended) to run fingers through it, according to the majority. A thin beard is one where the skin is visible beneath it.