Can I share a diagram with someone who has no account?

Yes. A read-only link needs no account; an edit link invites them to create a free one.

Yes. Create a share link from Share… on the diagram's File menu (Menu ☰ → File).

Anyone with the link opens read-only with no account, can expire, can carry a password and can be revoked at any time.
People signed in to ApexDiagram can be given Edit rights. Someone without an account gets an email inviting them to create a free one; once their address is confirmed the diagram appears under Shared with me on their dashboard.

Present… steps through the views full screen. Step-by-step: Share a diagram.