Replacing receptacles and found 14 AWG in a 20 amp circuit. Advice?
1) Your first question yes you should downgrade the circuit to 15Amps because the breaker protects the wires and if the breaker is rated for a higher current than the wires in the circuit can handle there is a fire risk.

2) If you were turn the one circuit into two circuits with a 20Amp circuit and a 15 Amp circuit with separate breakers then the outlet could be kept at 20Amps but otherwise no.

3) Maybe they ran out of the larger wire and that is just used what was around.