Questions about Trendnet PoE+ Gigabit Injector

Basically: In order for a PoE connection to be established, the source and the end device must first agree (detection) so that a device that does not support PoE is not accidentally damaged (-> Wikipedia). The circuit in the injector is dependent on the power supply from the power supply unit. Without power from the power supply, you have an unstable circuit hanging between the two cables and it is questionable whether the source and the end device can communicate correctly. Probably either nothing works or the terminal does not work properly. The manufacturer will certainly vehemently advise against such a configuration.

I think you mean "switch"? The answer would be "yes"! I have a Netgear Prosafe GS105PE on the second floor that gets power and bits from the Trendnet PoE+ Gigabit Injector in the basement.

Should theoretically work. I have the following comparable configuration in use: Camera - PoE Injector - WLAN Bridge. Camera is powered via PoE, bridge with power supply.