"Oh yeah, there's still one problem. If Anakin never learned how to become one with the force and all that, why does he show up as a Force Ghost at the end of Jedi? That still doesn't make sense to me..."

1) Becoming a Force ghost was about compassion and letting go. Keep in mind that Qui-gon never "learned" how to do it, either - it came as a result of his actions.

2) As to actions, Anakin a) was created by the Force and was the Chosen One, b) committed a tremendous act of compassion and self-sacrifice, and c) in doing so, fulfilled the prophecy and balanced the Force [presumably the whole reason for his existence in the first place.]