I have the following structure:
So in this case I have two different networks. What device can handle this structure, also PoE WiFi. In this case I have two measurement system attached in the PC B and PC C. The PC A is collecting the data and sending to the "master computer" through internet. In the future I would like to build up more measurement system. My question is, what kind of device can handle this structure(2 networks)? A router can handle this task?
You need a "Router" to connect to the internet, and a PoE enabled "Switch" that plugs into the router, and everything else then plugs into that.
You may be able to find a product that comprises both of those things, but logically they'll be seperate.
Or a wireless router!
P.S You don't have two separate networks. You have one network, that is partly wireless.
The best way to do this is with two or three separate devices. You'll find that attempting to extend the range of some kind of wireless access point / router combo will probably A) not work in connecting PC C in with the rest of your devices or B) the connection will be unreliable.
I recommend that you purchase dedicated hardware for a wireless bridge. You don't need anything heroic as 1km isn't very far for a directional point-to-point wireless bridge but you're certainly not going to get stable and reliable results using a wireless access point that you've jury-rigged into a bridge of some kind. There are many vendors in this market, with products in different price ranges (and PoE is a common feature). You can often mix and match your radio and antennas to get the best fit for your requirements and budget. We use Airayas for this in our network (and except for their broken SNMP implementation) they've been great.
You can simply connect PC A and PC B with a switch (make sure you got one with some kind of management capability) and use a router provided by your ISP or purchase/build your own router. I don't think very highly of the reliability of most COTS/SOHO routers, but the mid-grade business ones seem to be stable enough (Pfsense is also a great option!). PoE-enabled switches are often substantially more expensive than their non-PoE counterparts, so if you only need to support one device with PoE a PoE injector will be much more cost effective.
"Device" needs to provide switching. It more than likely needs to provide routing, and possibly NAT. Anything from your consumer Linksys type boxes on up should be able to cover that.
As for PoE, you don't need that provided in the device. You can add that externally as an intermediary device: https://www.google.com/search?q=poe+injector
That will free up your options considerably.