Can an Alchemist's familiar throw a bomb or fire an explosive missile?

Question

I'm in a Pathfinder game with an alchemist and there is a debate going on whether the alchemist's monkey familiar can fire a crossbow loaded with an explosive missile. Can it?

Answer 1

No, not with just this feat.

From the Explosive Missile feat:

As a standard action, the alchemist can infuse a single arrow, crossbow bolt, or one-handed firearm bullet with the power of his bomb, load the ammunition, and shoot the ranged weapon. He must be proficient with the weapon in order to accomplish this.

All three 'actions' (infusing, loading, and shooting) are all part of the same standard action. The feat doesn't allow you to infuse an arrow to use later, the infusing is part of the action which culminates in you, the alchemist, firing said arrow. If you don't fire the arrow, you can't infuse the arrow.

There might be an exception due to some other feat combination (a specific overriding general case), but not with this feat alone.

Answer 2

No. As written, it is all one action to infuse the missile and attack. There is no point at which the monkey could be holding a crossbow with an infused bolt and have the opportunity to attack with it.
(You might be able to get away with the monkey disarming as a readied action immediately before your attack roll, but then

1. The monkey has no further actions
2. What happens to the bolt if the action which imbues it is interrupted halfway through is undefined

That said, it might be a reasonable house rule.