Depends on what you mean by sync. It has limited support for tethering a mobile device to a computer on the same LAN, but lacks the kind of independent multi-device support that's a available in e.g. Matrix.

They don't, and I think they argue it's a security feature.

It is, at least, intentionally designed that way, for better or worse.

You can get per-conversation sync by joining multiple clients to the conversation.

It's one of those things where you'd probably want to be less secure and always sync to all devices.