I have an Extra license. Is it legal for my dad (who has a Technician license) or my mom (who is not licensed) to operate FT8 on 20 meters using my call sign, if I am physically present at the control point?
Apparently, yes. See Part 97, Amateur Radio Service Rules: 97.3.a.47 and 97.115.b. The FCC does not appear to make a distinction as to whether the third party is licensed or not.
Third party communications. A message from the control operator (first party) of an amateur station to another amateur station control operator (second party) on behalf of another person (third party).
From the FCC's own FAQ:
Q: May I allow the third party to speak the words of the message during the transmission of a third-party communication?
A: Yes. You may allow the third party to participate in stating the message by speaking, typing, telegraph keying the words of the message, pointing the video camera or by whatever means the message is generated. Section 97.115, however, prohibits you from allowing the third party to so participate where the third party is a prior amateur service licensee whose license was revoked; suspended for less than the balance of the license term and the suspension is still in effect; suspended for the balance of the license term and relicensing has not taken place; or surrendered for cancellation following notice of revocation, suspension or monetary forfeiture proceedings. The third party, moreover, may not be the subject of a cease and desist order that relates to amateur service operation and which is still in effect.
The key words here are: "or by whatever means the message is generated".