I will try to answer your questions.
I think either option would likely work as long as your switch has enough current to driver POE to each BomeBox. In generally POE is usually one way connection so if the ports on the switch are POE Out it should work but if they are POE in, it likely would not. There is usually circutry in the POE chain to prevent power from going backwards through the chain. You would need to check with your switch manufacturer to be sure that the either ports you are connecting to BomeBoxes from your switch provide POE out.
Computers generally do not accept POE since they have their own power so I would imagine the wires that connect power are internally disconnected on the computers.
There should not be any network latency in either scenario unless introduced by the switch itself.
BomeBox is not a network switch, rather is a router. By default the 2 ethernet ports are on the same network so no routing is necessary.
Depending on your switch speed for every port, you might just want to connect POE out from one switch port to the first BomeBox and then daisy chain the other two from there if they are all on the same network. BomeBox allows for 100Mps so if you want to drive them each at 100Mbps then you should probably go with one of your diagrams. I would not think higher speeds are necessary, however with MIDI traffic.
I found this interesting article on POE limitations that you might want to review. They are generic and not specifically BomeBox related.
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