Why am I being billed for Cloudwatch when I have NO running instances, no used storage, no active services of any kind?

Have a look at https://aws.amazon.com/cloudwatch/pricing/

CloudWatch doesn't just bill for gathering metrics from running services but also for having dashboards and alarms created and for gathering and storing logs and some other things. The storing of logs can stack up costs quite quickly.

You will have to clean up those other CloudWatch components as well, and make sure that no other unexpected service like CloudTrail is pushing logs through which you should be able to tell from the log group name.