Can a higher classed character decide to teach a lower classed character how to perfect a skill or feat thus bringing up the level of the lower level character simply through teaching / study?
It depends on the game. From the context however I'll assume you mean Dungeons & Dragons .
And the answer there is: it depends. Optional rules exist for such mentorship, but they're optional. It is up to the Dungeon Master of a particular game whether or not it is possible.