You do need an internet connection in order to get updates, yes! You can either bridge your computer’s WiFi with internet to the ethernet connection going to the BaseStation, or connect the Raspberry Pi WiFi to a network with internet access - WiFi icon in the upper right.
4.4.0 is the latest version of ArduRover.
You will only see extensions appear if you have an internet connection! Your screenshot shows that BlueOS is connected to WiFi, but it doesn’t have internet access (globe with slash going through it.)
Once connected to internet, please update BlueOS to 1.2 beta8 - enable pirate mode for this option to show up under BlueOS Version menu. If you’re still having issues when loading the default parameters, checkout this thread - if you flashed the BlueOS image yourself you need to add a lights.lua file.