Aeshuura
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It should. It is not a 3rd Party Product, it is a Pathfinder prestige class, but does not fall under the OGL and required to be placed on the PRD. You have a couple of choices, you can purchase the PDF of Paths of Prestige (which would be ideal) or check it out on d20pfsrd.
Check with your GM, and make sure that he is aware of the prestige class, before you go ahead with it though. That is always the safest bet.
| Zog of Deadwood |
Well, it's not Pathfinder Core Rules and it is campaign setting specific, so very likely not, depending on how your GM defines "strict". However, if he's running a PF game that IS set in Golarion, I would think it should count as legal (it is in a product made by Paizo specifically for use in Paizo's Pathfinder game when it is run in Paizo's Pathfinder game setting).
In general, though, GMs don't like allowing options from books they don't have...
| Are |
Essentially, the only thing that matters is what your DM means by "strict Pathfinder".
If he means "Core Rulebook only", then he won't allow this.
If he means "Hardcover rulebooks only", then he won't allow this.
If he means "No third party sources", then he should allow this, as it's from a Paizo product.