Re YouTube: do you actually need a Google account to use it? Check out #HookTube
too - all the YouTube content without using YouTube. A Firefox extension is available to replace all YouTube links and embeds with the equivalent HookTube one.
And +1 for Nextcloud calendars. It allows read-only and read-write sharing options, multiple calendars, multiple devices, and a pretty good web interface. On Android, #DAVdroid
is the best option to sync your calendars (and contacts) - there's an option in the Nextcloud app settings to help you set it up too. I'm sure there'll be something similar for Apple devices.