Yes. The Mark of Mastery is as much a test of character as it is of skill.

[He definitely would want to pass knowledge on to as many new Keybearers as possible, but rushing things could have bad results. Shoddy education can lead to a Keybearer turning to darkness instead...and shoddy education is something he's already afraid he did.]

For the Keyblade itself. It is extremely versatile. [And he figures that she's already seen him or Aqua using the gliders.]