For the my.example.com exposing real IP, you can simply turn on Cloudflare HTTP proxying (i.e click on the cloud icon in cloudflare dashboard to make it become orange). Cloudron will automatically adapt to this change.
For the wordpress issue - Delete the www CNAME record in namecheap. Then go to Cloudron dashboard and click on wordpress app's configure button (the wrench icon that appears when you hover over the app). Then in the Location tab, there is a redirections section. Add www there as a redirection. With that done, you will be able to access www.example.com.