Do I understand correct that a Persona is the representation of only a User in the Matrix ?
Persona can be a user, yes. Whenever you are connected to the matrix (which is pretty much all the time) you will have a matrix persona in the matrix. The representation of "you".
Having said that, all Persona Icons does not only have to be actual users. Persona Icons can also be agents, Sprites, ICs....
Persona icons are typically humanoid sized.
Do I understand correct that a PAN is not a Persona?
In this edition the book seem to make a distinction between your PAN icon and Persona Icon, yes.
PAN is some sort of HUD you see in AR
No real difference between AR and VR and book talk about two different type of "PAN"s.
At some pages it talk about the PAN as the Icon that represent most of your wireless electronic devices you have on your physical body. At other pages they talk about PAN as the network between your master device (commlink, cyberdeck or RCC) that have a small number of slaved devices (which can be very far from your physical body as there is no magic 'handshake range' in this edition).
PAN and Persona have no interconnections except the device they are created on, do they?
Book is not very clear on this matter, but this seem to be correct, yes.
So looking at a person in AR I can see only his/her Persona, if he/she is logged into the Matrix, do I?
No matter if you use AR or VR you typically see a human sized persona icon with a bunch of smaller device icons attached to it and a bunch of file icons attached to them.
Default for most matrix observers is to filter out most of the devices and files (merge them all into a single PAN icon), but if they want they can choose to see every single file and every single device.
If a PAN is in Running Silent mode, will all the slaved devises are also going to be in this mode too?
In 5th edition you spot individual devices, place your mark on (gain access on) individual devices and you run individual devices in silent mode.
In 6th edition you spot all devices in a network, you gain access on the whole network (including all its devices) and you run your whole network in silent mode.
