Do alchemists count as spellcasters for purposes of the Craft Magic Arms and Armor and Craft Wondrous Item feats, or do they have to take Master Craftsman first?
They have to take Master Craftsman first.
All the sensible ones will and do it with Craft Wondrous Item because that gives them all the dusts, unguents, etc.
If the latter, would being able to prepare a given extraction count as being able to cast it as a spell for purposes of crafting prerequisites?
I would say yes.
If an alchemist gets a wizard's spellbook, he can copy out formulas into his formulary if they're spells that are on the alchemist's extract list. That would point to them being the same magic
Can the Elixir of Life discovery be combined with the Extend and Eternal Potion discoveries to lenghten or eliminate the time limit on the effect of drinking the elixir?
Elixirs aren't potions, so I would say no.
Would the resurrecting elixir created from a philosopher's stone and a cure potion count as an actual elixir of life if the alchemist also has that discovery, allowing him to get the same benefits from drinking it?
It's actually a magical oil, not an elixir, even though it has the same effect.
It would be a judgement call from the GM, but I wouldn't see much wrong with saying yes, so long as the character has the elixir of life discovery.
When the Swift Alchemy and Instant Alchemy class features refer to "alchemical items", does only mean things created with a Craft (Alchemy) check, or does it apply to, say, potions?
It means stuff created with a Craft (Alchemy) check that are non-magical items, so basically acids, explosives, poisons, antitoxins and so on.
If an alchemist chooses the Eternal Youth grand discovery, does he still die naturally upon reaching his maximum age?
No. He dies when he gets killed. He doesn't have a maximum age.
Thanks in advance for anyone who answers. I'll post again if I think of any more.
No problem.