Check engine light comes on and off, rough idle....

What is your question?

My rpm normally sits around 500 when I am either idle, at a stop light, or in park. As of recently, it has begin to drop below the 500 then essentially knock or thump and then raise up to 1500 or so for a second or more then settle back down to repeat the process. The issue does not happen when I am in motion driving. When I put it in reverse and idle backwards (without pressing gas pedal) it will jerk, jerk, jerk while rolling backwards. The issue seems to diminish greatly (although not entirely (rpm jumping around is less intense than the <500->1500) when the AC unit is turned off. When the ac is turned off I start to smell a musty wet and somewhat warm air. When I drive for a long period (day or more) without the ac on, the knocking is less and the check engine light goes off. When I turn on ac for extended period, the engine will again knock and the check engine light comes on. Does anyone have any idea what is going on?

What makes this problem better or worse?

worse when engine is in reverse idle, worse when AC is turned on

How long has your 2016 Mazda CX-5 had this problem?

I have been going back and forth for a couple months