Hi Eldaria,
The "Running in server mode" and "hooray!!!!!!!!!!!!!!!!!!!" , "connection established" & "root" these logs will appear when you login to A+'s local web page from any WiFi or LAN clients. Here "root" is your login password & using that its connecting to dynamic update service running on A+. "Callback Received" comes when the zigbee/z-wave stack gets any packets from any zigbee/z-wave sensor. Here you have devices with Dev id 1, 2, 3, 4 & 5, I don't know what is the device type but they are sending "false" as sensor update.