Can you just use one side of Airpods and leave the other side at home? Because I usually just use one side of the Airpods, so that I am aware of the environment whenever I exercise or in a cafe, can only one side of the Airpods be used independently, while the other one is left at home?

So if one side of the Airpods is lost for some reason, you can still use the other side independently?
Yes, AirPods can be used independently in only one ear.

I use only one AirPod the majority of the time. Great for mono podcasts and for environmental awareness as you're walking around.