I use Radicale and find it great, but there's no UI, so you need to use whatever client you want that supports CalDAV (I use Lightning and the calendar on my phone). Lately I've been liking Nextcloud a lot, and that's a one-stop solution for lots of things, so nowadays I would recommend that if you have a home server or want to pay someone to host it.
Yeah, you do. As I said above, Fastmail's calendar is very good too, and you can load your self-hosted/CalDAV calendars into it, so that's a good option.