You can connect your 12v DC mains to this socket and power the RAK7249(This socket is for 12V DC);
2.Of course,you can keep the backup battery connected and 12V will charge battery;
3.No,usually the output of battery connects to DC socket.If you connect your 12V DC mains to this socket,how can you connect the output of battery to the socket also?Actually,if you use PoE to power RAK7249,the regulator on board will output 12V,12V (Parallel connection with the output of solar)will charge battery,the battery’s output connects to the DC socket.If PoE failed,the board will switch to battery automatically.
If the battery is connected to the top socket on the picture, marked “Backup Battery 12v”, and the incoming 12V is connected to the barrel connector bottom right on the picture, marked “? 12v ?”, which is what appears to be the original question, does this allow for the battery to be charged and take over if the incoming 12V fails?