But the one you might want to consider instead is called PipeWire. It implements the ALSA, Pulse and Jack APIs with a single implementation and it's pretty much the future of audio (and video casting) on Linux.
If you're using Wayland, you're already using PipeWire, but likely not for audio. On Fedora you can follow the instructions here https://fedoraproject.org/wiki/Changes/DefaultPipeWire which basically boil down as "uninstall pulse and install these packages" and you'll be using PipeWire for your audio.
I had tried several times to switch to it and it was not ready, but about a week ago I've been able to make the move with no loss in functionality and even got a fix to an old bug that affected my sound card, so at least with version 0.3.22 I can recommend giving it a go. Switching back to Pulse if bugs arise is trivial anyway.
Zoom on sway works, but since sway runs on top of Wayland and Zoom doesn't have the bindings to communicate with Wayland, I'm fairly positive screen sharing would not work. At least, not out of the box ... it might be possible to connect it to some other screen capture process if you're adventurous.
PulseAudio runs on top of ALSA. Traditionally, Linux desktop applications connect with ALSA and you can still manage ALSA directly. More recent applications, such as Zoom, expect to connect with Pulse and don't support connecting directly to ALSA.
From a user perspective, Pulse offers some advantages like being able to manage audio levels for different applications independently. In early releases, Pulse was unstable and difficult to troubleshoot, so it was easier just to use ALSA directly. Pulse has gotten a lot better in recent versions.
Yes and yes. Source: I run Zoom with i3.