Can I import my customer email list, and who am I allowed to email?

Yes, as long as everyone on it agreed to get your emails. Under Email Marketing → Contacts, import a CSV with an email column (names and tags optional), up to 10,000 at a time.

Before it imports, you confirm that they agreed, that they're in the United States, and that the list wasn't bought, rented or borrowed. Sending to people who didn't agree breaks the law (CAN-SPAM), gets emails marked as spam and pauses sending for your account. People who unsubscribed, bounced or reported spam are never added back.

Your list also grows on its own: people who tick to get your emails on a lead magnet or form become contacts, and they confirm by email first where you've asked for that.