Can you recover my data after the account is cancelled?

Ask before you cancel rather than after. What can be produced depends on the service and the plan, so assume nothing.

I cancelled by mistake. What now?

Open a ticket immediately and say so. Every route back gets narrower with time.

They are separate things. Check the domain's own renewal status.

Download them anyway. Your accountant should not depend on a login you may lose.

It covers files and databases. Mail, DNS records and invoices usually need their own export.