Climate control and radio acting strange

Hi all. So I have two issues. My climate control will sometimes not respond to the inputs from the user interface. It seems that the AC is on, but the blower is not blowing. I say this because if I set the AC to not recirculate, I can feel cold air being pushed in. If I hit the center console hard enough, or if I hit a hard enough bump in the road, the blower will kick on. Where should I start troubleshooting?

My second problem is my radio. It acts really weird sometimes. The screen will go blank, or will display random characters. Sometimes if I switch from the AUX to the radio, it will get stuck on the radio and won't go back to AUX no matter what I do. Also, the lights will randomly turn on/off while I'm driving at night.
I'm hoping these are common problems with a common cause. Thanks y'all.