I can highly recommend mailbox.org. I have been using their service for multiple years with my own domain and never had any problems sending or recieving mails from the big providers. They also take the privacy of their users data really seriously.

Can their contacts and calendar be synced with Android?

Yes, at least CardDav and CalDav are supported[0]

[0]: https://mailbox.org/en/your-personal-office

Yes CalDav, CarDAV and ActiveSync are supported[1]. On Android you could use DAVx5 to integrate it seamlessly into the system.

[1]https://kb.mailbox.org/en/private/account-article/data-synch...

I've been using Mailbox.org for nearly 2 years now and are happy with them, never had a problem. Hosted in Germany, you are able to use your own domain + catchall if needed.

Maybe a Nextcloud instance would match your requirenments. It allows sharing to users or externals via an URL and it has a not too bad UI + Apps.

mailbox.org also provides the functionality to use your own domain and a have a wildcard entry, where all emails go into your inbox.