Does shutting down VM within the host incur costs

I've noticed that if you shutdown a VM from within the OS (only tested this on Windows VMs), in the Azure Labs virtual machine admin console it shows that the VM is still running. Even with the auto shutdown VM when a user disconnects setting doesn't apply in this situation (actually, I checked the https://docs.microsoft.com/en-us/azure/lab-services/classroom-labs/how-to-enable-shutdown-disconnect and it does warn that this is the case so don't rely on it in this situation).

My questions are:

• Does this indicate that the VM is still being charged?
• Is the best option to tell users to not shutdown the VM but stop it from the Azure Labs web interface?
• Would a good option be to disable the shutdown option from the start menu. Would this help  to ensure the Auto-Shutdown when user disconnects kicks in as the only option is to close the RDP session if you're done with the lab?