A:
To answer your question NO.
That is not how PoE works.
In my experience PoE is a way of powering a device so that you do not need a power adapter and a receptacle to plug it in. There is a PoE converter that plugs into your power source that should have 2 ethernet plugs on it, one is input and one is powered output. You would use a patch cable to come out of this switch and go to the input of your PoE converter then another patch cable from the output side to your device that you are trying to PoE. You do not run form the PoE converter into the switch.