I'll let someone else with more experience comment on the problems with your interpretation of unarmed strikes. I'll comment on the one synthesist thing I know about:
3a- Moot question. One of the reasons why synthesist is overpowered is because you can sacrifice your summoner's HP to take the damage for the eidolon's temp hp pool. That means that you effectively only have 1 hp pool (coming from 2 sources), and never run out of eidolon HP until your summoner passes out.
This could even allow a single level dip in summoner to be used, since you can just use the HP from your other classes instead (rather effective for monks- you can put your point buy into mental stats, take the eidolon's physical stats, and just grab some natural armor boosts to still end up on top).
For the rest of synthesist stuff...eh...I have trouble seeing people touch that with a 10 foot pole. Sorry, it is just a REALLY troublesome archetype.
1a - An unarmed strike is not considered a natural weapon aside from being affected by certain spells and class abilities, even if augmented by the improved unarmed strikes feat. All IUS does is allow you to count as armed when using unarmed strikes, allow effects that affect manufactured weapons to apply to them, and increase the damage they deal.
1b - He needs at least enough limbs to have one natural attack on each, but I don't believe he can have more than one on each. You could feasibly have him with a bite and two claws/slams/pincers and not grow any additional limbs, but I believe that'd be the limit before you need to start growing horns for a gore attack or extra arms, wings, tentacles, etc. Think of it like this: if you have clawed hands and are a trained martial artist, you can't rake at an enemy with your claws and punch him at the same time. You could do one or the other, but not both simultaneously, since each requires a different method of attack and a different position of the hand. If you want to make the most out of natural weapons, IMO, either get as many as you're allowed by growing extra limbs, heads, tails, whatever, or make sure you have exactly one so you can add half again your Str mod instead of only half.
2 - I don't believe so. It applies to your eidolon's natural attacks, not yours, so unless your eidolon specifically has unarmed strikes, I doubt you could get away with this. Even then, it wouldn't work for the synthesist since the eidolon has no feats of its own.
3a - While fused, your eidolon's HP is temporary HP, not actual HP. As such, aside from the exception listed, there's no way you can heal the eidolon with a cure spell. In addition, you can't specifically target your eidolon anyway; since you're fused, you're one single target, so the cure spell would recover your HP, not its. If you really want to keep your eidolon's HP up, let the damage go through its temporary HP via the fused link ability and heal yourself with a cure spell. But that kind of removes the point of having turned your eidolon into a living armor, doesn't it?
3b - More than likely not, since fast healing affects regular HP, which your eidolon doesn't have in this state.
4 - Since it doesn't mention saves, I would assume the synthesist uses his own saves. However, you get to apply your eidolon's Dex and Con mods to Ref and Fort, respectively, since you're using its physical ability scores and mods instead of your own.
The question is hardly moot. I realize that he can sacrifice hps so the Eidolon doesn't die. This is about healing after a battle or during if it's needed. Since it doesn't regen naturally, you don't want to run around with only half your potential hps, you want to top yourself off before the next battle.
I view it as moot since you can just use your summoner hp until you are down to 1 hp, and only then start using eidolon HP. So you can just have most of the damage that needs healing down on your healable caster.
If you run through two health bars in a fight, then you have other problems. d8+con is seen as enough for entire melee classes. So you should rarely even lose more than a couple of eidolon HP per fight, as long as you heal up the summoner hp used between each one.
You already have what is potentially the largest healthbar in the entire game. Having it be a bit wonky is a small price.
I would Like to see any mention of this in the rules. Take into consideration1a - An unarmed strike is not considered a natural weapon aside from being affected by certain spells and class abilities, even if augmented by the improved unarmed strikes feat. All IUS does is allow you to count as armed when using unarmed strikes, allow effects that affect manufactured weapons to apply to them, and increase the damage they deal.
Some creatures do not have natural attacks. These creatures can make unarmed strikes just like humans do. See Table: Natural Attacks by Size for typical damage values for natural attacks by creature size.Meaning that it could make natural attacks, just like humans as a natural attack, Improved just means that they are proficient with it.
http://www.d20pfsrd.com/equipment---final/weapons/weapon-descriptions/strik e-unarmed
It is implicitly stated right there in the description of unarmed strikes that an unarmed strike is not a natural weapon. There are a lot of spells an effects that will affect both natural weapons and unarmed strikes, but that alone doesn't change that an unarmed strike isn't considered a natural attack.If you are assuming he can't use the Improved Unarmed Strike, that is true, it is dependent on the ruling on 1A
1b - He needs at least enough limbs to have one natural attack on each, but I don't believe he can have more than one on each. You could feasibly have him with a bite and two claws/slams/pincers and not grow any additional limbs, but I believe that'd be the limit before you need to start growing horns for a gore attack or extra arms, wings, tentacles, etc. Think of it like this: if you have clawed hands and are a trained martial artist, you can't rake at an enemy with your claws and punch him at the same time. You could do one or the other, but not both simultaneously, since each requires a different method of attack and a different position of the hand. If you want to make the most out of natural weapons, IMO, either get as many as you're allowed by growing extra limbs, heads, tails, whatever, or make sure you have exactly one so you can add half again your Str mod instead of only half.
I'll concede that, if you take away all of an eidolon's natural attacks, it'll utilize unarmed strikes. I'm not saying you can't do so even with natural attacks, just that if you make a natural strike with a limb, you can't make natural attacks with it, and vice versa. You're essentially "holding" your unarmed strike as a weapon. It doesn't make much sense logically, no, but this is game mechanics, so logic sometimes goes out the window.
The synthesist does state, that while they are fused, he can use all his own abilities. That would include feats/class abilities from other classes. He's pretty much in a big skin that increases his size. Since the Eidolon has access to everything the Synthesist does, I would think that would mean he could take it.
2 - I don't believe so. It applies to your eidolon's natural attacks, not yours, so unless your eidolon specifically has unarmed strikes, I doubt you could get away with this. Even then, it wouldn't work for the synthesist since the eidolon has no feats of its own.
Once again, I point to the fact that unarmed strikes are not natural weapons. As such, the improved damage evolution can't apply to an unarmed strike. Period.
3a - While fused, your eidolon's HP is temporary HP, not actual HP. As such, aside from the exception listed, there's no way you can heal the eidolon with a cure spell. In addition, you can't specifically target your eidolon anyway; since you're fused, you're one single target, so the cure spell would recover your HP, not its. If you really want to keep your eidolon's HP up, let the damage go through its temporary HP via the fused link ability and heal yourself with a cure spell. But that kind of removes the point of having turned your eidolon into a living armor, doesn't it?While the Eidolon's hps are considered temp hps, it is a suit pretty much and the temp hps is how they keep them seperate from each other.
In the spell Rejuvenate Eidolon, it states the spell cures 1d10 damage, so I would think a cure spell would do the same, unless it was the undead aspect to it.
Yes, it is how the two HP totals are kept divided, but doing so changes how the eidolon's HP works. It is no longer its own HP, but rather temporary HP you use to shield yourself from harm.
Under normal circumstances, rejuvenate eidolon would heal an eidolon's HP. But that's the whole reason it was stated specifically in the class feature as working differently in this case. Your eidolon no longer is represented with normal HP, it's with a pool of temporary HP.
I've heard arguments in all three ways. Unless someone can find some new quotes or errata, I doubt it will be settled on.
4 - Since it doesn't mention saves, I would assume the synthesist uses his own saves. However, you get to apply your eidolon's Dex and Con mods to Ref and Fort, respectively, since you're using its physical ability scores and mods instead of your own.
I'm basing this on general vs specific. In other words, if a rule is specifically stated to be different than normal (as in the case of casting rejuvenate eidolon), you follow the specific rule, but if no such alteration of the rules is stated, you follow the more general rules. Because nothing is stated about Ref, Fort, or Will saves, we default back to how things would normally go, in that we use our native save bonuses. However, it is specifically stated that we use the eidolon's physical abilities scores and modifiers, so while this may not directly change Ref and Fort, it does possibly change our Dex and Con modifiers, which are applied to our Ref and Fort saves.
Now, if you want to use a synthesist with unarmed strikes, it's not that hard. You'd just need to remove all of your eidolon's natural weapons. If you do that, it can benefit from improved unarmed strike and the VMC monk's damage dice. However, this seems like a pretty silly benefit when you could equip an actual weapon and grab some natural weapons and get more attacks that way.
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[Some creatures do not have natural attacks. These creatures can make unarmed strikes just like humans do. See Table: Natural Attacks by Size for typical damage values for natural attacks by creature size.Meaning that it could make natural attacks, just like humans as a natural attack, Improved just means that they are proficient with it.
How you get from "Some creatures do not have natural attacks. These creatures can make unarmed strikes just like humans do." to "human have a natural attack"?