My 2007 Ford Edge keeps lighting up the ABS light. It usually isn't on when I first start the car, but after a few minutes of driving it lights up and stays on.

I took it to Autozone and the C1446-20 code came up on a computer scan. I'm also having trouble every so often with shifting out of park. Im wondering if the two issues are related and if anyone has any suggestions on what to try fixing.

 

Google says the code is for the brake light switch, this would make sense with you having issues getting vehicle out of park.
I usually recommend complete electrical diagnosis first but honestly since its intermittent and a brake switch is cheap, just replace it and see if it fixes the issue.