Answering maraj219's questions from chapter 11, although I'm betting Chapter 12 took care of most of that...
> They need to find and destroy the horcruxes AND brew the invincibility potion?
Correct (ish). They need to find two horcruxes, one known (Nagini), one unknown, and Albus assumes Harry was inadvertently turned into one as well. They also need to figure out how to brew the counter potion to Merlin's Invincibility Potion. (Severus is on it.) And to make it as effective as possible (they're trying not to take any risks here), they'll need to employ the same artefacts for doing so. If all else fails, they could conceivably skip it, but as long as Albus was stuck searching through Tom's past for clues to the Horcruxes anyway, if he can use what he's learnt to get closer to those tools, well, it's too much of an advantage to pass up.
> Is Severus just trying to recreate the invincibility potion OR brew an antidote?
It's helpful to understand the Invincibility Potion because it provides him with clues to how the antidote must work, but he only needs to brew the antidote. The riddles that describe the potions are equally difficult, but there are more steps in the antidote, so that makes it harder, and that's what he's currently working on. The IP was also much easier to brew than the antidote, but it was more complicated to to take. But that's not Severus' problem. His problems are 1) figuring out the ingredients and brewing process (nearly done) 2) sourcing those ingredients without attracting attention (close), 3) brewing the damn thing (logically, he hasn't even started) and then 4) figuring out a way to get You-Know-Who to take it (at a complete loss). Albus put himself and Harry (and co.) on the other problem: if possible, recovering the artefacts You-Know-Who used to brew it for maximum efficacy.
> Have you specified the number of horcruxes in this story?
Albus told Harry two, and to the extent he'd mention it to anyone, that's the number he'd name. He is quite sure, however, that Harry is number three, and the audience knows this. (As that really only comes as a surprise the first time you read it in book 7, I saw no point to not revealing that earlier. Instead it'll give us a chance to see Albus' thoughts on the matter once in a while.)
> In chapter 001, when we find out what good ole Sluggy told Tom, was he saying the horcruxes were ONLY an option IF you could also brew the invincibility potion? Or was he saying something totally different and I missed it?
'Sluggy immediately high-handedly criticised Horcruxes as a solution if only one could brew [the] Invincibility Potion instead. Whatever that is. Hmm...'
If you can figure out how to brew the Invincibility Potion, you wouldn't need the much clumsier Horcrux approach to Sluggy's way of thinking. He's far less enamoured of murder than Tom, so he doesn't see a Horcrux as quite the solution Tom does, and he isn't accounting for the antidote to the Invincibility Potion (mostly because to the best of his knowledge it hasn't been done since the days of Merlin and Nimue) in that dismal of Horcruxes either. But given the Invincibility Potion wouldn't shred the practitioner's soul, even if all other things were equal, it still seems the better solution. Sluggy's is a purely academic response, he understands these things have been done, can be done, but has little to no idea how to do them himself, and no willingness to put the things he does understand about Horcruxes into play. And Tom is a belt and braces sort of a wizard, who didn't have the answers to the Invincibility Potion ready to hand at that point in time, and he went with the Horcruxes first while he worked on the potion. Just as well as he hadn't finished taking the courses of it before the Avada on Harry rebounded and would have killed him.
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> They need to find and destroy the horcruxes AND brew the invincibility potion?
Correct (ish). They need to find two horcruxes, one known (Nagini), one unknown, and Albus assumes Harry was inadvertently turned into one as well. They also need to figure out how to brew the counter potion to Merlin's Invincibility Potion. (Severus is on it.) And to make it as effective as possible (they're trying not to take any risks here), they'll need to employ the same artefacts for doing so. If all else fails, they could conceivably skip it, but as long as Albus was stuck searching through Tom's past for clues to the Horcruxes anyway, if he can use what he's learnt to get closer to those tools, well, it's too much of an advantage to pass up.
> Is Severus just trying to recreate the invincibility potion OR brew an antidote?
It's helpful to understand the Invincibility Potion because it provides him with clues to how the antidote must work, but he only needs to brew the antidote. The riddles that describe the potions are equally difficult, but there are more steps in the antidote, so that makes it harder, and that's what he's currently working on. The IP was also much easier to brew than the antidote, but it was more complicated to to take. But that's not Severus' problem. His problems are 1) figuring out the ingredients and brewing process (nearly done) 2) sourcing those ingredients without attracting attention (close), 3) brewing the damn thing (logically, he hasn't even started) and then 4) figuring out a way to get You-Know-Who to take it (at a complete loss). Albus put himself and Harry (and co.) on the other problem: if possible, recovering the artefacts You-Know-Who used to brew it for maximum efficacy.
> Have you specified the number of horcruxes in this story?
Albus told Harry two, and to the extent he'd mention it to anyone, that's the number he'd name. He is quite sure, however, that Harry is number three, and the audience knows this. (As that really only comes as a surprise the first time you read it in book 7, I saw no point to not revealing that earlier. Instead it'll give us a chance to see Albus' thoughts on the matter once in a while.)
> In chapter 001, when we find out what good ole Sluggy told Tom, was he saying the horcruxes were ONLY an option IF you could also brew the invincibility potion? Or was he saying something totally different and I missed it?
'Sluggy immediately high-handedly criticised Horcruxes as a solution if only one could brew [the] Invincibility Potion instead. Whatever that is. Hmm...'
If you can figure out how to brew the Invincibility Potion, you wouldn't need the much clumsier Horcrux approach to Sluggy's way of thinking. He's far less enamoured of murder than Tom, so he doesn't see a Horcrux as quite the solution Tom does, and he isn't accounting for the antidote to the Invincibility Potion (mostly because to the best of his knowledge it hasn't been done since the days of Merlin and Nimue) in that dismal of Horcruxes either. But given the Invincibility Potion wouldn't shred the practitioner's soul, even if all other things were equal, it still seems the better solution. Sluggy's is a purely academic response, he understands these things have been done, can be done, but has little to no idea how to do them himself, and no willingness to put the things he does understand about Horcruxes into play. And Tom is a belt and braces sort of a wizard, who didn't have the answers to the Invincibility Potion ready to hand at that point in time, and he went with the Horcruxes first while he worked on the potion. Just as well as he hadn't finished taking the courses of it before the Avada on Harry rebounded and would have killed him.