Yes, the power supply unit is included

This switch runs at 1Gbps. Check that the cable is at least cat.6 and the network card where you attach the other end of the cable must also be at least 1Gbps.

Sorry no idea, I bought it for the poe ports

It has C13/C14 compatible power supply.

Of course. Why shouldn't that be included? Netgear doesn't want to annoy its customers with an incomplete product from the very first minute. The data sheet that explains this is available here under Downloads. last page https://static.digitecgalaxus.ch/Files/4/1/1/4/1/1/9/2/300-Series_Unmanaged_PoE_DS.pdf

Sure... whether that makes sense in a specific case is another question. To answer that, you would have to describe in more detail what you are planning.