As for the armor, it's internal. Otherwise, you couldn't armor synthetic cyberlimb and still have people have to make Perception (3) tests to spot its artificial nature. It also explains the fairly large amount of capacity it uses up.
Can you take an agility enhancement from a leg and put it in a torso. Armor from a troll cyberskull skull and apply it to a gnome foot? There's noting in the rules that says you can't. It's just nonsense. (Well, let's face it, lots of things about cyber are nonsense. You can build a full cyberbody for a dwarf that has higher body and strength than one for a human, and it has the same capacity and everything?)
The point I'm trying to make here is that the same thing can be different for different limbs. Otherwise it's just numbers on a piece of paper, instead of a functioning piece of armor on an imaginary limb. So, maybe armor 1 in a synth hand is the same as armor 1 in an obvious hand, just serious internal reinforcement. But you can't put armor 2 in a synth hand. A synth half-arm, sure, and it provides protection up to the elbow. Why wouldn't Armor 2 on an obvious hand provide the same sort of protection? Anyway, that's just how I like to view things. I know its a game, and you sometimes have to sacrifice realism to make it work, but you don't always have to.
Also cyberlimbs should be fairly common in any era of shadowrun. They were suppose to be the go-to fix for a host of limb issues. Docks workers are suppose to be cybered enough that they don't use lift suits anymore. Thematically, they also fit it quite well even considering SR's shift from cyberpunk to post-cyberpunk. In older editions, they represented how people had to give up their humanity to keep with the cutting edge. In the current edition, they represent that have metal arms are cool and are way awesomer than normal human limbs.
Again, I'll point you to the book.
In today’s world of transplant-friendly bioware, the use of cyberlimbs is
sometimes viewed as crude and outdated. On the other hand, they are
cheap and easy to service and upgrade, so in the end they became even
more popular for the less fortunate. Additionally, since cyberlimbs are
capable of superior performance than natural ones and are compat-
ible with a variety of specialized technologies, this kind of cyberware
remains in high demand.
So, they are crude, outdated, low-class, and for laborers. In other words, (and this is all I've been saying the whole time, so, readers, please pay attention to this part,) they will penalize a character who has to infiltrate any high-class environment. They don't play well in Bellview or an arcology. They are an advantage which may limit the places a character can operate effectively as a potential dice pool penalty on social rolls and by drawing attention from security. This may not matter to many characters, but it matters to some.
I also think it's unlikely for people to freak out even if they did know they were armored limbs. First off, it's perfectly legal. You don't even have to buy a fake permit for it. Secondly, consider the wealth of armor and how even messengers can wear 6/6 jumpsuits, I think armor wearing is quite common. After all, this is a world were there are dogs that look like men and go on murderous rampages during full moons and violent gangs can operate in the fairly nice parts of downtown Seattle.
Wearing armor and being armor are two different things. Carrying a gun is normal. Having a gun, literally inside your hand, is not normal.
Balancewise, the issue isn't that mundanes can have a ton of armor. That's one of the few things mundanes have going for them. It just really kicks the other defensive ware options to the curb. You should become tough because you replaced your bones with metal like Wolverine or have kelver for skin and not because your doctor chopping off your hands and feet due to you coming down with diabetes.
Since bone lacing, othroskin, and dermal plating are a tad on the weak side regardless of the state of cyberlimb armor, I'll be for buffing them and then nerfing cyberlimb armor. My quick and dirty suggestion is to double the effectiveness of the defensive ware and then have cyberlimb armor on partial limbs only apply for that limb. This also will tend to increase the essence cost of being defensive enough that mundanes don't really care, but mages will. Thus it helps keep mages lower defenses relative to combat focused mundanes, but cybermages can still totally exist.
There are a lot of cyber options out there, but none of them are as effective as going robocop.
I don't think they should be. Getting a limb or torso made of or covered with R4 armor is better than a layer of sub-dermal kevlar. Having titanium bones won't protect you from getting shot in the liver. So on.
Location should matter, and a hand is not a vital area. Removing a whole arm as a viable target for small-arms fire is going to significantly protect about 12% of the body, (9% from the coverage of the arm and 3-4% from the arm's coverage of the side. A leg will get you about 18% of the body completely protected. The torso is just so much more surface and so much more important. It seems like there should be something to reflect that in the rules. Maybe some kind of curve of effectiveness. Dermal Sheath 1 protects many more important organs and blood vessels than any of the subsequent sheathes. But, it's kinda dumb that replacing your torso with a big metal shell of avali 20 armor plating isn't as effective as a kevlar vest. Maybe beefing up other cyber armor a bit, like the orthoskin is a good idea with some sort of diminishing returns, but robocop is not to be nerfed. Not ever.