If I learn a spell, do I add it the number of spells I know, or do I replace a spell I already know with it?
You add it to the formulae you “know,” but alchemists don’t really “know” formulae (and wizards don’t “know” spells) the way a sorcerer for example does.
The so-called “spontaneous” spellcasters, like sorcerer, gain a very limited number of spells known as they level up. Those spellcasters cannot (easily) add to this number. They know these spells innately, and require no external aid for them.
Other spellcasters, like wizards, are known as “prepared” spellcasters, and do not learn spells innately. Instead they require a spellbook (or a god/faith, in the case of divine prepared spellcasters), and even though they “know” every spell in their spellbook, they still need the spellbook to prepare those spells, and can only prepare a selection of those spells each day. On the other hand, however, they can easily add as many spells as they like to the spellbook(s). Thus, unlike spontaneous spellcasters, prepared spellcasters do not have a specific number of spells known. It’s just however many spells they have put in their spellbook.
Alchemists work much like a prepared spellcaster; instead of “spells” they have “extracts” and so instead of a spellbook they have a formula book. Aside from that, they work about the same: they can add as many extract formulae to their formula book(s) as they like. They “know” all of these formulae, but require the formula book to prepared them.
I don't add to the number of spells I can cast per day, correct?
Correct, the number of spells you know is completely independent from the number of spells you can cast per day. Alchemists and wizards must “prepare” their extracts/spells ahead of time, and because they can add as many formulae/spells to their books as they like, in any given day they won’t be able to prepare all of the extracts/spells they “know.”
As well, is there any specific type of spells that I can copy?
You can only copy spells that are found on your formula list. Wizard spells that aren’t on this list cannot be made into formulae and cannot be copied by an alchemist.