I am wondering, if I take a Ratfolk Alchemist/Ninja and give him the vistigial arm discovery, do I then qualify for the Multiweapon Fighting feat?
Is so, if it required that I fight with said extra limb? Would it be possibly to have, say, Wakizashi(main hand), wakizashi(offhand), tail blade(offhand?), dwarven boulder helmet(offhand?) and get a routine of Waki/Waki/tail/helmet?
Mechanically speaking, how does this work, is it possible to get 4-7 attacks per turn by using multiple weapons that each occupy a separate limb or am I restricted to iteratives only?
Vestigial arms doesn't grant you any extra attacks the way an actual 3rd (or 4th) arm would.
While not strictly clear, I don't think you would qualify for multiweapon fighting. You would need to play a kasatha to have a 3rd (and 4th) hand.
You only have 1 main hand, and 1 off-hand.
BAB will grant you main hand additional iterative attacks. Two Weapon fighting reduces penalties for using your off-hand. Improved Two Weapon Fighting grants an additional attack with your off hand, and Greater TWF grants yet another.
So, if you had a BAB of 11 and had Greater TWF you would have:
3 main hand attacks and 3 off hand attacks available to you.
Now, you can make those attacks with different weapons, so all you off hand attacks could be made with different weapons (though doing so is unlikely to ever be beneficial to you).
The Multiweapon Fighting feat only has a prerequisite of having 3+ hands, as far as I'm aware, not that the attacks be made with said hands. This is the main reason I'm asking.
The problem is that while vestigial arm grants a physical hand to do something with, it doesn't grant you an additional hand worth of effort.
You seem like you might be new to the board, so you're probably unaware that there is a paradigm which exist which creates a difference between the number of physical hands you have, and the amount of effort of things you can do. This came about specifically because of the alchemist's vestigial arm ability.
While there are many weapons that don't require the use of a physical hand, they still use up a hand of effort. See the boot blade as an example.
The boot blade uses up your off hand of effort despite, not being in your physical hand.
As I said, you have a specific number of primary hand attacks you can make and off-hand attacks you can take (which depend on your BAB for regularly granted iterative attacks and whether you posses the Improved and Greater TWF feats for additional off-hand attacks).
This FAQ may help you to understand the situation:
Alchemist, Tentacle/Vestigial Arm: What does "extra attacks" mean for these discoveries?
It means "extra," as in "more than you would be able to make if you didn't have that discovery."
For example, if you're low-level alchemist who uses two-weapon fighting, you can normally make two attacks per round (one with each weapon). If you take the tentacle discovery, on your turn you can make
* two weapon attacks but no tentacle attack,
* a weapon attack with your left hand plus a secondary tentacle attack, or
* a weapon attack with your right hand plus a secondary tentacle attack.
At no time can you make a left hand weapon attack, a right hand weapon attack, and a tentacle attack on the same turn because the tentacle discovery says it "does not give the alchemist any extra attacks or actions per round." This language is calling out that the tentacle is not a standard natural weapon and doesn't follow the standard rules for using natural weapons (which would normally allow you to make the natural weapon attack in addition to your other attacks).Likewise, if you instead took the vestigial arm discovery and put a weapon in that arm's hand, on your turn you can make
* a weapon attack with your left hand and one with your right hand,
* a weapon attack with your right hand and one with your vestigial arm, or
* a weapon attack with your left hand and one with your vestigial arm,
At no time can you make a left hand weapon attack, a right hand weapon attack, and a vestigial hand weapon attack on the same turn because the vestigial arm discovery says it "does not give the alchemist any extra attacks or actions per round."
The exact same restrictions would apply if your race had claws or you had some other ability to add claws to your limbs: the text of both discoveries says they do not give you any extra attacks per round, whether used as natural weapons, wielding manufactured weapons, or adding natural weapons to a limb that didn't originally have natural weapons.Remember that these two discoveries do not have any level requirements, and therefore are not especially powerful; permanently adding additional attacks per round is beyond the scope of a discovery available to 2nd-level alchemists.
Even if vestigial arm did qualify you for multiweapon fighting, it does not grant you any additional attacks. It only reduces the penalties for those additional off-hand attacks, in the same way that Two Weapon Fighting doesn't grant you the first off-hand attack it only reduces the penalties for making attacks with your off-hand. You need Improved and Greater TWF to get additional off-hand attacks.
Further, there is no Improved or Greater Multiweapon fighting which would grant additional off-hand attacks.
Therefore, even if you qualified for Multiweapon, it would grant you no benefit. Well, it would reduce the penalties you have for making off-hand attacks (which you don't have). It would basically function as TWF.