How can I check that I have properly stopped a virtual machine and that I am not being billed for it?
You can check the status of your virtual machines in the Virtual Machines tab and also in the virtual machine Dashboard. If virtual machine status says "Stopped," you are still being billed. Only "Stopped (Deallocated)" indicates you are not being billed. To ensure you are not being billed, always stop virtual machines from the management portal. You can also stop the virtual machine through Powershell by calling ShutdownRoleOperation with "PostShutdownAction" equal to "StoppedDeallocated".