These features are already present.
From the Help page, "You can get help with Groups.io from the articles below. If you'd like more assistance or have questions, please check out the Group Managers Forum."
see -> https://groups.io/static/features:
"Facebook - Post to your group whenever there is an update to a Facebook Page.", see Admin -> Integrations
see -> https://groups.io/g/GroupManagersForum/wiki/Sync-with-your-Google-Calendar
Please use this forum to request new features