[imcritic]

First inform us of mail providers that match the same criteria.

[randunel]

All, as far as I can tell.

[imcritic]

Is Gmail non-propietary? Can you self host it?

[randunel]

You can self host an email server, what you can't self host is proprietary features on top of those, but I'm pretty sure you can find alternatives that work with said email server software you picked to self host.