I prefer running the latest firmware, but if everything is working well for you and you don’t need the newest features or fixes, there’s no harm in sticking with your current setup.
Updating the firmware on Phantom 3 models can be quite a hassle compared to the streamlined process for newer drones released in recent years, which is another good reason to leave things as they are. If you decide to update it, you can find some useful guides here.
The most recent version of DJI GO is compatible with your drone. That download is available in the DJI Downloads.
We’re discussing that over in this thread. I haven’t seen any mention of that change being made in DJI GO, but it seems like it should be possible if it only requires a FlySafe database update. If an update is available, you’ll be prompted to download it in DJI GO.