Yes! Some instances have downvotes disabled, they will be discarded even when you or I downvote something that’s on their server.

yes, it might be out of sync sometimes due to federation but yes.

Yes and no:

Yes, votes are shared between instances. However, they aren’t synchronized. When you click on “upvote”, your server sends a message to the community with the requested change. The remote server applies that change, then sends messages to other remote servers with that update.

There are retries built in, but if for some reason one of those messages doesn’t get delivered, the different instances will get out of sync. I do not think there is a mechanism for “catching up” once this happens.

Yes

Should but barely does.

I feel like the mod of instances can choose how to sync

Asynchronous best-effort updates, further modified by individual instance policies. Attempts will be made!