Lets break down the original questions then shall we.
If I Probe/Back Door Entry a device that's not slaved (on a PAN or in a Host), the device opposes only with Mental Attribute dice of owner. Right?
Devices in general does no have a Firewall or Data Processing rating of their own. In order for a device to gain access to a Firewall rating it generally have to be behind a network that consist of a Host, Commlink, RCC, Cyberjack or Living Network. But of course if it happen to have a Firewall of its own then it get to use that when not connected to a network.
If it is slaved, I am opposed by the master dice pools. Right?
Yes.
SR6 p. 174 Devices
everyone has a commlink ... They are used for rudimentary access, most commonly for commcalls and searches, as well as basic Matrix Firewall defense for devices attached to the user’s PAN.You can't Probe/Back Door slaved devices directly, you have to hack the Master (Commlink/Cyberdeck/Host). Right?
Yes, but rather than trying to figure out master-and-slave-relationships you basically only need to understand which 'network' the device is connected to.
Some actions don't require access and can be taken towards a device directly even if the device is hiding behind a 'network'.
Other actions require that you first get into the 'network'.
If you successfully take the probe + backdoor entry actions against a PAN then you will be considered to be on the 'inside' which mean you now are free to take actions that require user or admin access (on anything that is connected to the 'network').
If I get access to the Master, I have that save level of access to all slaves devices. Right?
Yes, but again, rather think of it as you gain access to the whole 'network' rather than just a specific 'master device'.
SR6 p. 176 Matrix Access and Pans
On the user side, the Matrix is built around the Personal Area Network (PAN). These are networks composed of a commlink and/or a deck, with a small number of devices slaved behind it. Generally speaking, in order to get to a device attached to a PAN, one must first gain access to that PAN.The slave devices still get Master dice pools right, you just have the same access level to them as you have to the Master.
Yes, but again in this edition you don't really need to think about slaves and masters.
If someone is attacking a device in your PAN then it is you (matrix attributes of your matrix persona and mental attributes of your meat character) that is defending the device.