I actually have two answers for most your questions....
First of all PAN. We had, still have, the same issue in SR5 as in SR6 where, on multiple places the book (SR5), they talk about "PAN" as all of the (potentially hundreds) of wireless enabled devices you carry directly on your body and on other places in the book they talk about "PAN" strictly as a master device with a small number of slaves (such as drones) with no range limitation at all.
If we are discussing a strict reading of RAW then only Data Processing devices may be slaved to your commlink (in SR6) and strictly speaking only slaved devices count as being part of your PAN - which probably mean the Cyberlimb will be a stand-alone device.
If the cyberlimb does not offer any wireless bonuses of any kind then it will probably, just like in previous edition, not be a wireless enabled stand alone device (but if cyberlimbs work as in previous edition it will still be connected and controlled via your nervous system, not to be confused with DNI... should be a SR5 quote about this in the gear section that talk about augmentations).
Since it is not wireless enabled it will not have a device icon of its own on the matrix and since it is a stand alone device you can also not access it by gaining access to a PAN. For an observer it will lack device icon and no matter how many times he try he will not spot it.
If you get a direct connection to the cyberarm then you would be able to data spike it by just having Outsider access. It is also clear that you would be allowed to take the spoof command action (it too can be taken if you only have Outsider access), the question is rather if the device is allowed to perform the command or not while at the same time being directly controlled by its owner (in 5th edition manual control, remote control and jumped in control was overriding autopilot, at least when talking drones).
Via the direct connection you could also brute force or probe+backdoor entry to gain User or Admin on the stand alone device. With Admin access you could for example reboot it, even if the owner is currently using it. But again.... you need a direct connection for this so not very subtle I'd say.
After you gained User or Admin access on a network (or a stand alone device), Control Device is an action that you take on a specific device to gain the ability to remote control it, and then, if you are successful, you get extended control over the device similar to if you would be a legit user of the device (but again we get into the discussion if you are allowed to remote control a device that someone else is already controlling, for drones and vehicles it is clear from the rigger section in SR6 that you may only have one 'driver' and it is implied but never spelled out that the same thing holds for other devices --- in 5th edition it was clear from the rigger section that remote control on a drone override auto pilot and manual control, but that you could not remote control a device that someone else was already remote controlling and that jumped in control would override remote control).
The only reason I can see why you would want to have a wireless disabled device in network that is wireless exposed to the matrix is that the wireless disabled device will be immune to outsider actions such as data spike and spoof command for hackers that don't already have access on your network. Once a hacker is inside your network then it doesn't seem to really matter if the device is wireless enabled or connected to the network via a wire.
If you don't want to be hacked then you should probably disable all wireless, yes.
Your datajack comes with a 1 meter retractable cable. You can use that to create a direct connection with a stand alone device. This can also be used with another datajack to create a 2 part call that is very hard to hack or eavesdrop .