I was wondering: is it possible to run solo adventures for Pathfinder? In the Gamemastery Guide (I think), the authors seem to admit that the game is geared toward a standard four-person party of multiple classes. Would it be hard to run games for a solo character, then?

Also, a specific question - in the main rulebook, there's this formula for calcuting appropriate Challenge Rating for parties. Is this formula appropriate for solo characters? Meaning, the appropriate CR for an average-difficulty encounter for a solo character being that character's level?

BTW. I haven't really GMed Pathfinder before and I still need to read the book in its entirety. Is it a good idea to learn PF by GMing it, then? :)

You can do it, though it takes a lot of tweaking on the part of the GM.  The CR system is of only limited usefulness in its normal state, so it'd be nearly useless for a solo character.

In general, other systems are better for it, but it can be done.

I believe it is but I do not know how much fun it would be.

Just about any game can be a solo game.  It usually means more work for at least one of the participants if not both, but it's doable.

Certain playstyles within a game may be more handicapped by only having one player over others, but I can imagine there's a lot that can be done in a game like Pathfinder geared towards telling a story centered around 1 player's character.

PF's CR is similar to 3.5's, and they're both rather pointless. An encounter of CR X is supposed to be average for four PCs of level X...and the chances of that happening is about the same as winning the lottery. It depends on about a billion factors.

As for playing solo, it really depends on the class. I'd suggest a Druid or similar.

Gestalt and Hybrid classes are very good choices for a solo game also.