If I throw an acid flask or vial of holy water or any other splash damage type weapon, does the Slayer's Studied Target Bonus apply to attack and damage?
Yes, Studied Target applies. From Paizo, emphasis mine:
Alchemist's Fire: You can throw a flask of alchemist's fire as a splash weapon. Treat this attack as a ranged touch attack with a range increment of 10 feet.
Studied Target (Ex): A slayer can study an opponent he can see as a move action. The slayer then gains a +1 bonus on Bluff, Knowledge, Perception, Sense Motive, and Survival checks attempted against that opponent, and a +1 bonus on weapon attack rolls and weapon damage rolls against it.
\$\begingroup\$ That seems pretty reasonable from a RAW point of view. As a DM I would maybe question the bonus to damage just based on flavor, since studying something would not make your fire fierier, or holy water holier. But it is such a small bonus that in most cases it shouldn't matter. \$\endgroup\$– D.SpetzOct 8, 2015 at 16:39
2\$\begingroup\$ My concern—and why I didn't attempt an answer—is that I don't think Paizo has ever said that splash weapons count as weapons. Further, the developers' bad habit of adjective+noun items being different from just noun items (e.g. here) may apply in this case. Just something to consider before you sit down to, like, a Pathfinder Society game hoping this'll work. \$\endgroup\$ Oct 8, 2015 at 16:50
\$\begingroup\$ @D.Spetz It wouldn't make the fire fierier, but studying the target could help you to understand the most efficient way of using it. For instance, setting his boots on fire might not harm him as much as finding bare skin or a weak area of the armor. That's how I could see it justified, at least. \$\endgroup\$– duzzyOct 8, 2015 at 19:04