Can the Explosive Missile alchemist discovery be applied to alchemical cartridges?
I'm guessing "no" with exception to paper cartridges, which say they can be composed of a firearm bullet.
I would say No, as the Discovery states a "Firearm Bullet" which is a specified type of firearm ammunition.
Even if you could infuse a Paper Cartridge, utilizing the Discovery is a standard action, so you would lose the quick loading benefit of that ammunition.
Oh, that's right. I wonder if the explosive missile can be prepared ahead of time and fired later?
Likely No, because when you use the Discovery you infuse the bullet, load the weapon and fire it all as one standard action.
I think of it like Gambit's mutant ability. As a single attack, you pull out a card, infuse it with explosiveness, toss and enjoy.