[RPG] Can a character take a free action outside of their turn

Most free actions must occur on your turn, so no, the Dwarf cannot draw his shield

I quoted 3.5 in the other question, but since you're not interested in that, I'll stick with a reading of the Pathfinder PRD:

Combat Round:

In a normal round, you can perform a standard action and a move action, or you can perform a full-round action. You can also perform one swift action and one or more free actions. You can always take a move action in place of a standard action.

Free Actions:

Free actions don't take any time at all, though there may be limits to the number of free actions you can perform in a turn. Free actions rarely incur attacks of opportunity. Some common free actions are described below.

Great, free actions are quick. What's speaking?

Speak

In general, speaking is a free action that you can perform even when it isn't your turn. Speaking more than a few sentences is generally beyond the limit of a free action.

(Emphasis Mine)

So, why is there a special clause for speaking that says you can do it when it is not your turn if you can take free actions outside of your turn? This clause does not come into conflict with "You can perform one or more free actions while taking another action normally.", which is simply a clarification that "Sure you can drop your sword while attempting to climb the rope while shouting at your Dwarf companion to get his shield out"

How about immediate actions?

Much like a swift action, an immediate action consumes a very small amount of time but represents a larger expenditure of effort and energy than a free action. However, unlike a swift action, an immediate action can be performed at any time—even if it's not your turn.

There again is the special emphasis that it can be done when it is not your turn. This further implies that most actions can only be taken on your turn.

Paizo, to my knowledge, has not commented on this because it is the same as 3.5, and this has already been covered in a FAQ by the 3.5 designers. Since Pathfinder is an improvement on 3.5 and doesn't change the rules wholesale, why would they comment again on this?

Source? Pathfinder PRD combat section.

And for those interested, further discussion on the 3.5 side of things here: https://rpg.stackexchange.com/a/8896/1736

Edit

And to counter a point from your question:

This interpretation also makes sense stylistically, as a character should be able to take their usual free actions while already reacting to another character, such as drawing a shield while intercepting an attack or loading a crossbow with rapid reload while making an attack of opportunity.

What about during the surprise round? Say someone botches their perception and is about to get shot with said arrow. Totally unaware. Should he be able to whip out his shield then?

No. Unless you have some feat or special ability that allows you to take another action (be it a move action or standard action) during a move action, or an ability that let you open doors as part of another action, or allow you to do those actions as part of a full-round-action. Or a special rule that allows an exception to taking actions as another type of action, such as mount/dismount steeds as free actions with a DC 20 ride check, or channel energy as swift action as an attack action.

Otherwise, all move actions must start on square A and finish on square B, as long as your path isnt blocked in some way.

Alternatively, it seems that the intent of the game designers was that doors, unless they somehow block your path, shouldn't be that hard to open/close. We can read more about this on this post from 2009.

There is much discussion about "how long does one person takes to open or close a door while running" or "what kind of door is it?" or "what way does this door open". But, as a GM, you do have some backup on the rules if you decide that opening/closing doors should only take part of your movement instead of another move action.

Terrain and Obstacles

From tangled plants to broken stone, there are a number of terrain features that can affect your movement.

Difficult Terrain

Difficult terrain, such as heavy undergrowth, broken ground, or steep stairs, hampers movement. Each square of difficult terrain counts as 2 squares of movement. Each diagonal move into a difficult terrain square counts as 3 squares. You can't run or charge across difficult terrain.

If you occupy squares with different kinds of terrain, you can move only as fast as the most difficult terrain you occupy will allow.

Obstacles

Like difficult terrain, obstacles can hamper movement. If an obstacle hampers movement but doesn't completely block it, each obstructed square or obstacle between squares counts as 2 squares of movement. You must pay this cost to cross the obstacle, in addition to the cost to move into the square on the other side. If you don't have sufficient movement to cross the obstacle and move into the square on the other side, you can't cross it. Some obstacles may also require a skill check to cross.

On the other hand, some obstacles block movement entirely. A character can't move through a blocking obstacle.

You will see that many posters do rule it this way, opening a door takes 5 or 10 feet of movement instead of a move action. Personally, i would rule that if the door is open (ie: unlocked) it takes 10 feet of movement, if it's locked but you got the key, or if it's too big (like a double door), or too old (large dungeon metal or stone doors), it takes a move action.