I think I saw in another thread that the Almond+ has quite some power to spare. so as long as you don't have to much USB stuff like USB powered harddrives and similar connected I think you will be good running with POE.
You could probably spare some additional power by turning of stuff you don't use, (If possible) like If you don't use z-wave, turn that off, if you don't use 5GHz turn that off.
I don't have the router here (I'm at work)
As far as getting it power over ethernet, so as far as i understand you will need a POE adapter that will sit in the wall, which will feed the router with both power as well as an ethernet input for internet. But, how will it be connected to the ethernet on the other end "inside" the wall? That is more my concern.
POE will run along the whole length of the Ethernet cable, although I think it has some limits on how long it can be. But the idea is that you have power on the other end, so for example where you have your DSL modem or Fiber converter or whatever you connect the Almond+ to, you will likely have a plug, so this is where you inject the power to the POE.
I will like I said before probably not make a hole to insert the whole Almond+ into the wall, but I will probably try to hide the cables in the wall. I was also planning on having a battery pack close to the Almond+ to ensure power during a blackout so that the security and alarm functions continue to work when the power is out.