After searching the internet for the most suitable, self-hosted social networking system, I stumbled upon Dolphin by Boonex. I found out that their office is only 2 hours driving distance south of Brisbane. Thanks to Rakesh from Mumbai, India, an expert in this field, for helping over the last three weeks to configure this site. He is still doing some fine-tuning in the chat module. It is based on Rocket Chat. The transmission is very fast.