Audio-Video Conference App/Platform

Could you please suggest me a software/app or online service/platform similar with WhatsApp/Facebook Messenger/Skype able to make audio or video conference with more options:
-      I would like to have an administrator or more able to manage the session. That would imply to moderate the session, to control the audio of each participant, to schedule and prioritize the speaking time.
-      Normally we would like to let the audio7video control to each participant, but in some cases, we would like to have the administrator override rights and control who speaks.
-      To be able to share a common screen/file (text, audio or video file) in real time, so each participant can see the same info.
-      Make a schedule/summary in advance of how the conference will take place/evolve and to be accessible/viewable to each member on the app/platform.
-      To be able to invite to join from common social media platforms as WhatsApp/Facebook Messenger/Skype.
-      To be close group, only people with invitation, eventually password and user name to be able to join.
-      If it is a desktop combine with mobile software/app or platform would be the best.
-      Very important: it should be free and only if that is not possible, then we can think at a paid version.
Up to now we have tried WhatsApp/Facebook Messenger/Skype but they are not good enough. They are limited in the regards to the above required options, especially the part with administrator control rights and/or common screen file sharing in real time.
I think I have seen something similar in a webinars presentations, but I do not remember what platform was used