Questions about Netgear WAX204

I would try installing the latest firmware on the router. As far as this security warning is concerned, in principle it's nothing dangerous, it just means that the manufacturer probably doesn't use an up-to-date certificate, but nothing can happen in that sense, because it's a local IP address. What I could also recommend is to return and then buy the Xiaomi AX3000 WiFi router, this router is very fast and also has new WiFi 6, it can manage up to 256 devices and can also be expanded to a very strong mesh WiFi (up to 10 devices), a single costs about 80 and a Seit with 2 costs about 130 francs. https://www.digitec.ch/search?q=xiaomi%20ax3000 These Xiaomi routers have a built-in 3 port Ethernet Gbit switch.

Yes, the router supports bridge mode

You determine the name of the WLAN and the password yourself in the configuration of the AP.

But it can't do PoE, so it can't be powered that way either. Have a look at Downloads --> Technical data sheet --> last page

Hello. If a router is already present and a LAN connection / cable is available at the place where the device is placed, then you can use this device well.