If I run more than one business in BytePhase, do they share one Mailchimp account?

Yes. Mailchimp is connected once for your whole BytePhase workspace, and customers are shared across businesses, so every business pushes contacts to the same Mailchimp account. You still choose the audience for each push by its Audience ID, so you can keep a separate audience per business, or use one audience and tell the businesses apart with tags.