Help calculating witch attack with prehensile hair

Question

Level 8
BAB 4
STR 7 (-2)
INT 26 (+8)

Hex: Prehensile hair

Even though it is listed as a secondary natural attack, I would just use the hair to attack as a standard action. How would I apply the STR mod as it’s only form of natural attack? Is this how I would calculate the attack modifier and damage?

Attack: +12 (BAB 4 + INT 8)
Damage: 1d3+12 (INT 8*1.5)

This wording from the universal monster rules might be relevant:

If a creature has only one natural attack, it is always made using the creature’s full base attack bonus and adds 1-1/2 times the creature’s Strength bonus on damage rolls. This increase does not apply if the creature has multiple attacks but only takes one. If a creature has only one type of attack, but has multiple attacks per round, that attack is treated as a primary attack, regardless of its type.

Answer 1

You can use your Prehensile Hair as a Primary Natural attack if its your only Natural attack.

While its true that Prehensile Hair references that it's a Secondary Natural Attack, this is a formality not an overwrite. It's only indicating that because it falls under 'Other' on the Natural Attack table, it is typically a Secondary natural attack. This only applies if you have other Natural attacks such as Claws or a Bite, or when using manufactured weapons as well (in which case all Natural attacks become Secondary).

The Universal Monster Rule is the more specific rule in this instance, and does allow you to make a BAB attack for STRx1.5 (INTx1.5 in this case) attack if you don't posses Claws, Bite, etc (as well as do not attack with manufactured weapons).

Note In a strange caveat, even possessing another Natural attack negates this benefit, whether or not you're using them.

The nail in the coffin is that Prehensile Hair does not say that it can only be a Secondary Natural attack. It only says what it is. As with the many creatures that have Secondary Natural attacks that fall under the referenced UMR, the UMR alters that 'normal' state. Additionally, if you're forgoing the ability to cast a spell, attack with a weapon, and any other Natural attacks, it's fair to allow you to deal 1d3+INTx1.5.

Answer 2

Secondary attacks are made using the creature’s base attack bonus –5 and add only 1/2 the creature’s Strength bonus on damage rolls.

And, using Prehensile hair, a witch:

can manipulate her hair as if it were a limb with a Strength score equal to her Intelligence score. Her hair has reach 10 feet, and she can use it as a secondary natural attack that deals 1d3 points of damage (1d2 for a Small witch).

So, being a secondary natural attack, the hair attack would be:

Attack: +7 (+4 BAB, +8 INT-as-STR, -5 secondary attack)
Damage: 1d3 + 4 (8 INT-as-STR * 0.5)

Note, however, that a witch

with natural attacks and attacks made with weapons can use both as part of a full attack action (Natural Attacks)

So that same witch could also attack with, say, a dagger at +2 (+4 BAB, -2 STR) for 1d4 - 2 (STR) in the same round as the hair attack (and, of course, could use feats like Weapon Finesse on the dagger attack).