Fibre vs Copper short Distance

Neither, really. Replacing a copper link with a fiber link might lower latency a tiny bit (assuming an uncongested link), but what you really get when you replace a "core" link with a higher bandwidth link is less possible congestion. In your example scenerio, it doesn't matter, because there is only one device on each end. In a live network, though, moving from 1g to 10g core links will ease congestion problems within the core of the network.

Now, as a side affect, you may get lower latency and better traffic flow, but that is purely due to easing congestion so the routers/switches aren't overloaded and dropping/queueing traffic.

IEEE 802.3af POE has two modes, mode A sends power on the "data pairs" while mode B sends power on the "spare pairs". However that is not very relevant as it doesn't sound like you are planning to use that. It sounds more like you are planning a "Ghetto POE" type setup.

I wouldn't worry too much about mixing POTs and Ethernet on the same cable, especially if the POTs link is only local. I also wouldn't worry about CAT5 vs CAT5E on a link this short.

The bigger problem would be current on the DC power lines. 35W at 12V is nearly 3A. Apparently the safe current limit on the conductors is 350ma so if you used one conductor for power and one for ground you would be running nearly 8 times the acceptable current on each conductor. Even if you used the whole cable for power and ground you would still be running at over double the acceptable current.