We are jitsi specialized software development company. We can help you with your requirements. Find our feedback below regarding each point.
Start live stream - We need to configure jibri with your required RTMP endpoint on separate servers
Open Shared Document - We need to setup etherpad
Invite someone - Jitsi does give you an invite option. But if you need a more sophisticated solution like sending out an email invite we can build it
Add scheduling with global time zone - Need more clarification on this as to whether you need a separate portal or build on top of jitsi. Either way it could be done
Add meeting password - This is available already. But you need to pre-configure a meeting password we can help you out
Add virtual background - This is also available out of the box. Have you built the frontend yourself using lib-jitsi-meet?