Can a formula be learned from a potion as long as it's a learnable formula?
You can use a Formula Alembic to learn the formula of a potion.
Does having a potion, and knowing what it is, allow me to recreate the potion using Brew Potion as outlined for my class?
No. You need to be able to prepare an extract to make something into a potion.
Can I know a formula before I'm at a level that I am capable of using it in an extract or potion?
Yes. Though, if you're poor, I'd avoid it. Scribing it into your formula book costs money. Table of costs here.
Take a look at the Alchemical Allocation extract, which is a 2nd level extract and thus available to you at 4th level. That extract would enable you to drink a potion and then spit it back out into its container, with the result that you gain the effect of the potion but still have it. That doesn't let you learn the formula for that potion as an extract, but it could be very useful.
I was looking in vain for a feat or discovery that would let you do what you wanted, but little did I know it could be done with a very cheap magic item as described above.
Generally, most APs assume that any statted town uses the magic item availability detailed here. Can't help you if your DM doesn't use that system but it's set up that way in the pre-made stuff to help unusual classes like the Alchemist that might want items that aren't a part of loot tables. It improves the game experience, IMO, and it's worth asking your DM if they'll use that set of rules.
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Thats useful actually, but yeah that item is really what I need. Now I just need to find out how to buy it, or get both Craft Wondrous Item and Identify feats to be able to craft it.Take a look at the Alchemical Allocation extract, which is a 2nd level extract and thus available to you at 4th level. That extract would enable you to drink a potion and then spit it back out into its container, with the result that you gain the effect of the potion but still have it. That doesn't let you learn the formula for that potion as an extract, but it could be very useful.
I was looking in vain for a feat or discovery that would let you do what you wanted, but little did I know it could be done with a very cheap magic item as described above.
An alchemist is very limited when using Craft Wondrous Items:
Alchemist: Is an alchemist a spellcaster 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.
RAW you need to learn Master Craftsman to be able to craft a limited selection of Wondrous Items.
The discovery spell Knowledge gives you a caster level, even if it is for a single spell, so it should allow you to take the crafting feats (ask your GM first).
Wondrous Items allow you to ignore non-feat requirements when crafting them in exchange for a +5 to the DC to craft the item. Most crafters would have no problem making it at a DC 13 instead of 8 - you can take 10 on crafting IIRC, so just a single rank and class skill bonus in Spellcraft is an auto-success. The extra requirement of Brew Potion is a lot harsher than the Alchemist requirement.
In this case, since the alembic is a wondrous item, the craft feat you absolutely need is Craft Wondrous Item. The Brew Potion feat and identify spell, and even the need for the creator to be an alchemist, can all be skipped for +5 DC each. (I realize you personally don't need to skip the first and last of those, but it explains how a non-alchemist spellcaster could manage this w/o much trouble.)
You're going to need to wait to Level 4 before you can craft a potion of invisibility anyway, and when you do, you can just select invisibility as one of the formulas you get for free. Why not just use the potion of invisibility as a potion of invisibility? You may be poor but the 150 gp you get from selling it is small compared to the WBL you're accumulating from Level 2 to Level 3.
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Wondrous Items allow you to ignore non-feat requirements when crafting them in exchange for a +5 to the DC to craft the item. Most crafters would have no problem making it at a DC 13 instead of 8 - you can take 10 on crafting IIRC, so just a single rank and class skill bonus in Spellcraft is an auto-success. The extra requirement of Brew Potion is a lot harsher than the Alchemist requirement.So if I am understanding you right, as long as I added +5 to the DC needed to make the item and expended the GP required, I don't need the Craft Wondrous Item and Identify feats?
The crat feat is always needed.
You could take 5 skills ranks in Craft (Glass), Master Craftsman and Craft Wondrous Items and be able to make any wondrous items that are made of glass, but it is terribly inefficient.
As I said above the discovery Spell Knowledge give you a caster level, so it should allow you to take Craft Wondrous Items and use it to make any wondrous item, but it is a bit iffy.
Some GM treats alchemist as spellcasters with a caster level, so maybe you will not even need the discovery.
To sum it up "Ask your GM".