Electrical – 14-2 Tap Branched From 12-2 Feed on 20amp Circuit…What To Do

I have a switch by my front door that supplied power to a receptacle. I want to wire that switch to an existing ceiling fan/light combo in the same room. I've already made the outlet constantly hot. The switch currently controls nothing. I inspected the wiring situation in the attic to see how the fan was getting power and what my options were for running 14-3 from the fan to the switch. Here is what I found.

The person who installed the fan tapped into a 12-2 wire that feeds a dining room outlet with 14-2 cable to the fan. This outlet is on a 20amp circuit, which also supplies another dining room outlet and 3 kitchen backsplash outlets. The splice was just out in the open in my attic. I fixed that by containing the entire splice in a properly grounded metal box mounted to a ceiling joist, but now I'm wondering if I should replace the tap wire that runs to the fan with 12-2, since it is on a 20amp circuit and then run 12-3 from the fan to the switch. Would there be any issues with the fan unit wiring not being 12g wire on this circuit? I haven't had any issues with the fan wired this way in the 10 years I've lived in this house, but now that I've seen how this is wired, I want to make sure it's all up to code. The person who wired the fan didn't even contain those connections in a fixture box. They are also just out in the open in the attic. I'll have to install a proper ceiling fan mounting box.

Thanks for any help.

Josh