How can I see whether an administrator manually added or edited a punch?

There are several ways:

1) Go to Manage => Punches, and in the Filter section, select Status=Overridden. When you open an override punch, expand the Advanced section, and you'll see who overrode it and what the original times were (if they were edited from clock punch)

2) Go to Reports => Audit Time, and select your filter criteria. More info here on the Audit Time report:

https://support.fareclock.com/hc/en-us/articles/360040202633-How-do-I-view-an-audit-log-of-all-changes-made-by-users-

3) Go to Reports => Time Cards, and select your filter criteria. Added punches will have a red 'A' next to them, and edited punches will have a red 'E' next to them.