Can you also use it to test an RJ45 socket in the wall? For example, connect one device to each socket with two short cables.
And second question: Can I use it to check whether the cables are PoE-capable?
Yes, I use a similar device for this. Of course, you then test both RJ-45 sockets plus the cabling.
Which power can be transmitted over which distance depends on the wire cross-section and whether the cable is shielded or not. This device is not able to do that. It only tests whether there is a correct connection or whether cables are crossed or short-circuited.