We are unable to duplicate the issues using your steps or us trying a variety of clients attached to accounts and sending thousands of messages while chasing flags and deleting messages etc. We can't duplicate any bad behaviors. If you would like us to test further, we would need an account exhibiting the behavior.
The new sub folder not showing up in Thunderbird was reproducible. Thunderbird does act differently with subscriptions to folders.
Tim Uzzanti
CEO
SmarterTools Inc.
www.smartertools.com