Yes, creatures can attack anything within their natural reach
As you pointed out,
Creatures that take up more than 1 square typically have a natural reach of 10 feet or more, meaning that they can reach targets even if they aren't in adjacent squares.
Unlike when someone uses a reach weapon, a creature with greater than normal natural reach (more than 5 feet) still threatens squares adjacent to it.
So what does "threaten" mean?
You threaten all squares into which you can make a melee attack, even when it is not your turn. Generally, that means everything in all squares adjacent to your space (including diagonally).
As a visual illustration that natural reach doesn't exclude adjacent squares (or just to visualize reach in general, especially diagonal reach) these graphics can be helpful as well.
In searching for answers to this, I've come across an interesting point on the Paizo forums. If you are in one of the far corners and you consider these not threatened, then you can diagonally move towards the character and never provoke an AOO (that is, per RAW)... and yet, logically, a threatened area should make an uninterrupted circle around the creature. This may explain why 3.5 made an exception out of this.
Yes, that is precisely why 3.5e made that exception, and it’s also why Paizo issued an official FAQ that changed Pathfinder’s rules to add the same exception, as @caps reports in this fine answer that you should go upvote.
Thus, a reach weapon can attack the following \$X\$’s from \$C\$:
\begin{array}{c|c}
\phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} \\ \hline
& X & X & X & X & X & \\ \hline
& X & & & & X & \\ \hline
& X & & C & & X & \\ \hline
& X & & & & X & \\ \hline
& X & X & X & X & X & \\ \hline
\\
\end{array}
Before the FAQ change
However, the FAQ entry that caps reports did not exist at the time this question was asked. At that time, you did not get the four corners, and so could only attack these \$X\$’s from \$C\$:
\begin{array}{c|c}
\phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} \\ \hline
& A & X & X & X & & \\ \hline
& X & B & & & X & \\ \hline
& X & & C & & X & \\ \hline
& X & & & & X & \\ \hline
& & X & X & X & & \\ \hline
\\
\end{array}
Here, it would appear that someone could step from \$A\$ to \$B\$ to avoid an attack of opportunity altogether. However, even before the FAQ just changed this to be like 3.5e, the developers at Paizo had ...for lack of a better word, we’ll call it a clarification, though it honestly just confused me more. From an earlier FAQ:
Can you or can you not attack diagonally at a distance of 2x squares (15'=10' exception) with a reach weapon?
James Jacobs: Nope. A reach weapon gives a specific extension to your reach. When you count out squares, since every other square is doubled when you count diagonally, that means that there’ll be corners where you can’t reach.
Sean K. Reynolds: It's an artifact of the grid. The closest the rules come to addressing this is in Large, Huge, Gargantuan, and Colossal Creatures, which says:
Unlike when someone uses a reach weapon, a creature with greater than normal natural reach (more than 5 feet) still threatens squares adjacent to it. A creature with greater than normal natural reach usually gets an attack of opportunity against you if you approach it, because you must enter and move within the range of its reach before you can attack it.
So just because the grid has a square for "15 feet away" and a square for "5 feet away," but no square for "10 feet away," using that corner path doesn't mean you're magically teleporting from 15 feet to 5 feet; you are passing through a 10-foot-radius band around the creature, and therefore you provoke an AOO.
Admittedly it's not clear, and obviously it doesn't have the diagram in the 3E book to provide a non-textual example, but it's supposed to work as I described above.
Basically, the idea was, under the rules at the time, you didn’t threaten 15 ft. away, so you don’t get the corner, but you did threaten 10 ft. away and there’s no way to move from 15 ft. away to 5 ft. away without passing through a point that is 10 ft. away. Thus, someone moving from 15 ft. away on the diagonal to 5 ft. away on the same diagonal was going to provoke even under these rules.
So the enemy at \$A\$ moving to the point marked \$B\$ towards \$C\$ with a reach weapon provoked an attack of opportunity (assuming this isn’t a 5 ft. step of course), because somewhere between \$A\$ and \$B\$, there is a point that is 10 ft. away from \$C\$ that the enemy has to pass through.
Presumably, you would have adjudicated the enemy’s position for the purposes of the attack of opportunity as being \$A\$, though this was never made clear. In this sense, the end result was identical to the 3.5e/post-FAQ version for movement towards you: creatures leaving that corner square to enter a square inside your reach provoked an attack of opportunity as if you threatened that square. You were not eligible to make an attack of opportunity if the enemy performs any other action that provokes from \$A\$, including movement in other directions, because you do not actually threaten it.
This was a headache. Even before the FAQ changed things to match 3.5e, that was precisely what I recommended:
Reach weapons are one of the few fairly-nice things that melee can get. There’s really no need to nerf them. I strongly suggest that you straight-up ignore this nonsense and use the 3.5 rule. The exception to the usual calculation of ranges in the case of reach weapons is weird, but clearly there was a good reason for it: without it, you wind up with this mess.
![pathfinder reach range[1]](https://i.stack.imgur.com/hWGKA.png)
Best Answer
The question's first diagram's xs correctly indicate the area threatened by a Medium or littler level 1-3 white-haired witch's white hair. The question's second diagram's xs and Xs correctly indicate the area threatened by a Medium or littler level 4-7 white-haired witch's white hair and the area threatened by a Medium or littler witch that's employing the hex prehensile hair. Below is further clarification of these abilities.
White hair
The witch archetype white-haired witch's supernatural ability white hair says
A creature with this class feature threatens squares adjacent to its space with its white hair, a natural attack, no matter the white-haired witch's size. For example, a Tiny white-haired witch normally threatens no squares and a Large (tall) white-haired witch normally threatens adjacent squares and squares 10 ft. from its space, but both white-haired witches threaten only squares adjacent to their spaces with their white hair.
The supernatural ability white hair continues, saying
Thus the white-haired witch increases the distance from its space that it threatens with its white hair by 5 ft. to 10 ft. at level 4, from 10 ft. to 15 ft. at level 8, from 15 ft. to 20 ft. at level 12, from 20 ft. to 25 ft. at level 16, and, finally, from 25 ft. to 30 ft. at level 20.
Unlike a creature with a typical reach weapon like a longspear, the white-haired witch threatens with its hair all those squares, functioning, essentially, like a creature with natural reach except that, for example, the Medium white-haired witch can typically only make attacks into squares beyond adjacent squares with its white hair.
Obviously, folks laugh at high-level white-haired witches that lack both a high Dexterity score and the feat Combat Reflexes.
Prehensile hair
The witch hex prehensile hair, a supernatural ability, says
A witch employing this hex threatens with its prehensile hair, a natural attack, squares adjacent to its space and 10 ft. from its space no matter the witch's size. For example, a Tiny witch normally threatens no squares and a Large (tall) witch normally threatens adjacent squares and squares 10 ft. from its space, but both witches threaten adjacent squares and squares 10 ft. from their spaces when employing the hex prehensile hair.
Note: Because these distances are set by the special abilities themselves, their specificity trumps the more general rules about reach. For instance, a Medium white-haired witch shouldn't see its white hair threaten an even bigger area if the white-haired witch is the subject of an enlarge person spell (although such a witch will see the area threatened modified due to the white-haired witch occupying more space for the spell's duration). However, a generous GM may rule otherwise.
Also, typically a white-haired witch just can't take the hex prehensile hair, the white-haired witch's supernatural ability white hair replacing the witch's class feature hex.