[RPG] Does a Pathfinder Witch’s Slumber Hex Count as Mind-Affecting Effect

First off, don't forget that there's a Sleep spell in the main book that uses Thaumaturgy (YS 293), which would make a good baseline.

Apart from that, it looks about right. I'm not sure you'd want to have the Aspect be "Terribly Sleepy", since invoking that wouldn't actually put them to sleep. Invoking an Aspect that implies something will happen when invoked (such as say, "Off Balance") doesn't make that happen; it just makes it easier for someone to make it happen. Invoking "Off-Balance" won't automatically knock someone over, you'd still have to roll Fists or Athletics or whatever to actually knock them over; invoking the Aspect would get you the +2/reroll making it much more likely.

It might be better to have the Aspect be "Light Sleeper" or "Catnapping", since that puts them out straight out (which is what you you want), but still lets people invoke to get a bonus to sneaking or whatnot, but at the same time implies that the target can be woken up easily.

Probably.

There has been no clarification on the ambiguous "as if you had used Diplomacy" language. In general it's accepted that you can lay the Charm Person spell on someone, improve their attitude further with Diplomacy, and since those are two separate effects, when the spell fades they're left with however many levels of attitude improvement the Diplomacy did. As the Charm hex is of small benefit (1 level improvement) and short-lived (albeit a standard action and near undetectable), I see no reason not to allow it. Do note that the Charm hex works on animals and humanoids but Diplomacy only works on humanoids (whose language you can speak) so you'll need Handle Animal to get more out of animals.

Also if you're going this route please notice that before Helpful, there's additional checks required to get them to do things (with the Charm Person spell these are replaced with opposed CHA checks):

If a creature’s attitude toward you is at least indifferent, you can make requests of the creature. This is an additional Diplomacy check, using the creature’s current attitude to determine the base DC, with one of the following modifiers. Once a creature’s attitude has shifted to helpful, the creature gives in to most requests without a check, unless the request is against its nature or puts it in serious peril. Some requests automatically fail if the request goes against the creature’s values or its nature, subject to GM discretion.