The proliferation of different install methods made it impossible for the devs to support every method. See ADR0012. Debian is the officially supported Linux flavour as long as strict guidelines are adhered to. Other distros are not officially supported but will work in most cases, you only get community support though.
Yes but it is now called Home Assistant (OS).
Up to you. If you want an easy to maintain “appliance like” install with supervised addons, yes. If you need to tinker with the base OS then one of the other install methods may suit you better.