1. In the 'last engaged' area, which profile actions count as an engagement?
This is the list of engagement possibilities: form submissions, event registrations, started/submitted applications, touchpoints, logins in the portal, 1on1 emails, workflow emails and campaign emails (after being opened).
3. If a profile receives an email, does that count as an engagement?
No, it only counts as an engagement when the profile opens the email.
2. Can I change the Source Method of profiles?
No, you cannot. The Source Method is recorded when a profile is created, and can't be changed afterwards.