Net3 node as iso

Opto isolator? I'm not sure what you mean - it's an Ethernet to DMX convertor, so you can basically pretend it's a remote 'rear face' of the console.
-The DMX ports on a Net3 DMX Gateway are optically isolated from each other and the PSU, and feature switchable termination.

All Net3 Gateways can be powered by PoE, as can the RFR Base Station.

Any PoE injector compliant with IEEE 802.3 can be used. Gateways use less than 5W of power each, so you will need to be sure that the chosen unit has a sufficient rating to supply the number of Gateways you are going to have.
(Note that early Cisco PoE may not be compatible as they created their own method before the IEEE standard was finalised)

ETC generally recommend switches with PoE built-in, simply because they are easier to install (not so many patch leads), but injectors may be better if they are being added to an existing install.

In regards to the question of opto splitting, the short answer is yes.

Net3 Four Port DMX Gateways running in Net3 mode can have one port set to input and as long as the other three ports are patched to the same universe, you will recieve the same  DMX output levels on the other three ports with or without connection to the network. GCE (Gateway Configuration Editor) is required to assign the port universes as well as change DMX port modes to input or output as appropriate.

Please be aware though, if you are connected to the network and have levels from another source patched to the same universe of sACN, the gateway will use the assigned priority of the sources to determine winning levels. 

As a bit of extra information, by default multiple sources will HTP on a Net3 system.  For purpose of backup  and override, we also give the flexibility to assign sources higher or lower priority.