I’m going to call the Basic/Expert/etc line “D&D”, distinguishing it from O(riginal)D&D (the white box), and A(dvanced)D&D. D&D is therefor the game we played last Sunday.
Demihumans and character classes
Demihumans can choose to be a different character class, so you are allowed, e.g. Elven Fighters or Halfling Thieves, and are treated exactly as any human of that class (including for level maxima) but:
1) You still must meet all the racial minima to be of that race
2) You get none of the special abilities of your race, which are assumed to come from training that you’re neglecting in order to learn the abilities of your new class, except:
a) Dwarves and Elves retain their infra-vision
c) Halflings retain their Save vs. Death Ray/Poison, and Halfling Thieves retain their racial Hide abilities.
The D&D rules forbid Magic Users letting other magic users copy spells from their books, but don’t really explain it except as a cultural prohibition (nobody wants to risk their spell-book); to make this more concrete, copying a spell from a Magic User’s book into another book erases the spell, the same way copying a spell from a scroll uses up the scroll. Magic Users teach their apprentices spells by creating a scroll with the appropriate spell, which the apprentice can then copy into their spell book per the usual rules.