Trying to connect 12/3 wire to switch powered by 14/2 wire
I am installing a ceiling fan. I ran new 12/3 wire for the fan. The existing switch in the wall is powered by 14/2. I want to run the lites off the switch and the fan with constant power. Can I tie the black source wire to my black fan wire & then pigtail that connection to the bottom screw on the switch, and then connect my red fan wire to the top screw on the switch, giving me switched power to the red wire & constant power to the black wire? Also, this is on a 20 amp breaker, is it okay to use 12 gauge wire tying into the existing 14 gauge wire?