How does one wash the hands up to the elbows in Wudu': Is it by scooping water with the right hand and passing it over to the left, then washing, or by scooping water with the right hand and pouring it directly onto it? And is it permissible to wash the hands under a tap? And must the direction of washing be from the elbow towards the palms and not the other way around?

What is obligatory in ablution (wudu') is to deliver water to the ablutionary organs by any means, and the important thing is for the water to reach the entirety of the organ that must be washed.

As for starting with the palms of the hands, it is a sunnah (prophetic tradition). If one were to start with the elbows, it would suffice, as Al-Mawardi stated in "Al-Hawi": "If he started from the elbow to the fingertips, it would suffice him."

The correct view is that the sunnah is to begin with the fingertips absolutely, as mentioned in "Tuhfat Al-Habib," where it states: "And among them [meaning, among the sunnahs of ablution] is to begin washing one's hands with the fingertips, even if someone else pours water on him, as affirmed by Al-Nawawi in his verification, contrary to what Al-Saymari said, that he begins with the elbow if someone else pours water on him."

Therefore, what you were told is incorrect.