
Cerberus Seven |

So for example:
Arcane Strike or Weapon Focus or even Specialisation?
Officially, I believe so. It's an attack roll to throw one and, when their BAB is high enough, an alchemist with the Fast Bombs discovery can take a full-attack action with his bombs. So weapon focus and the like should apply.
Now, the question of whether Arcane Strike works on bombs is tricky, because, officially, alchemists aren't really true arcane casters. Your GM might rule it's allowable, since the damage bonus compared to the bombs themselves will end up being incredibly measly.
CalethosVB |

I would argue myself that Arcane Strike would count because an Alchemist has a caster level for the purpose of things like dispelling bombs, and effects targeting things being affected by one of his elixers (dispel magic, for example).
You can take Weapon Focus for anything in the game that requires an attack roll (unarmed strike, grapple, (or Ray if you are a spellcaster). However, you can't take Weapon Specialization, or greater Focus or Specialization unless you also have the requisite levels of Fighter or equivalent.

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@Nikolaus Athas
Alchemist Bombs
Bombs are considered weapons and can be selected using feats such as Point-Blank Shot and Weapon Focus.
As for arcane strike splash damage? No. Look at the Alchemist link above and here...
Splash WeaponYou can apply direct hit damage to the target only. The splash effect is not modified and comes as a product of the weapon only. Fortunately, bombs do amazing splash damage. I am not convinced you can apply this feat to a splash weapon at all, but the wording does not prohibit it.

Cerberus Seven |

As for arcane strike splash damage? No. Look at the Alchemist link above and here...
Splash WeaponYou can apply direct hit damage to the target only. The splash effect is not modified and comes as a product of the weapon only. Fortunately, bombs do amazing splash damage. I am not convinced you can apply this feat to a splash weapon at all, but the wording does not prohibit it.
Are you sure about that? The splash damage from a bomb is equal to the minimum damage a bomb would do. That means it takes into account modifiers from Good Hope, Point Blank Shot, etc. What makes Arcane Strike different?

GreenMandar |

I would argue myself that Arcane Strike would count because an Alchemist has a caster level for the purpose of things like dispelling bombs, and effects targeting things being affected by one of his elixers (dispel magic, for example).
You can take Weapon Focus for anything in the game that requires an attack roll (unarmed strike, grapple, (or Ray if you are a spellcaster). However, you can't take Weapon Specialization, or greater Focus or Specialization unless you also have the requisite levels of Fighter or equivalent.
That would be inconsistent with the FAQ ruling on alchemists crafting magic items. While spell-like ability caster levels count as being able to cast spells for prereq purposes, alchemist caster levels don't.
Alchemist: Is an alchemist a spell-caster for the purpose of crafting magic items other than potions?
As written, no, alchemists are not spellcasters, and therefore can't select feats such as Craft Wondrous Item.
The design team is aware that this creates some thematic problems with the idea of an alchemist creating golems and so on, and plan to examine this in the future.—Pathfinder Design Team, 03/01/13

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@Cerberus Seven I am fairly sure. This answer about Point Blank Shot from the FAQ also supports the intent behind Splash Damage.
Point Blank Shot: Do I add the feat's extra damage to the splash damage from a splash weapon?
No, the extra damage from Point Blank Shot only applies to the target of a direct hit with a splash weapon (including direct hits from an alchemist's bomb).—Pathfinder Design Team, 05/24/13
Alchemist bombs are very strong already. They do not really need any kind of damage boost.