No. You can only connect one Confluence to a database at a time.
You'll need to find/write a synchronisation service to do that.
Technically, Confluence Data Centre does many instances, but it looks like a single Confluence installation, it's not an "exchange of data", it's everyone working in one Confluence.
Theoretically yes, if you use the remotepublishing plugin from Comalatech. I have used it one direction to publish from an internal server to an external public server. Not sure I would try bidirectional as collisions would be an issue, and this publishing would be on-demand, triggered by event. This plugin also requires their Workflows plugin (which I have also used successfully).
You could write a workflow that would publish a page once it is updated, for example. But arbitration would be really hard.
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