I looked through a few pages and couldn't find anything relating to my topic, and I'm sorry if I'm repeating a previous topic, but does Natural Knowledge of the Path grant you the free access spells?

It is treated in every way as if you invested a number of "free" Magic Levels into the Path. Note that his also means that the levels gained through Natural Knowledge will cause a penalty to any opposed Path (so if you take Natural Knowledge of the Path in Necromancy, you're either only going to be a Necromancer or you should take the Advantage that removes the opposed Path restriction).

One thing I don't know - if I have Natural Knowledge of the Path in, for instance, both Earth and Air, are they both at the same rank, or is one of them halved? It's an interesting question.

Yeah, you get the free access spells. Natural knowledge Path is a great advantage. Since you get about as many level in a path as most character can ever get total. And you get them all as soon as you start. Remember, the rules recommend that a GM should not let a player spend all their magic levels during creation. So a character with Natural Knowledge of the Path doesn't start with twice as many spells (and twice as high if they concentrate) as a wizard without it, they start with closer to four times as many spells.