I have not worked with IaaS instances using Linux yet, but I think I can answer some of them based on my understanding of how the infrastructure as a whole works.
When you create the virtual machine, you have an OS disk (which maps to your root above, and I believe that it boots, although I think it is a Linux-based artifact and does not exist when using Windows). This OS disk is stored in the Windows Azure BLOB as VHD, Page BLOB. Same thing with the created 20 gigabyte data disk. These are disks that will be safely stored and ONLY these disks.
1) In your power-off test, did you actually uninstall the deployment or just disconnect it? Shutting down the virtual machine will leave it deployed (and therefore on the same physical machine). Just being turned off doesn't stop you from being blamed because it is actually still deployed. If you delete the deployment and then create a new deployment, later pointing to the same drive with the OS and data that you created (you will find them in your gallery), you will get a better idea of what happens if the virtual machine is moved from -for self-healing, as it will be very common on another physical server. See below why I think the "resource" drive is stuck.
2) You are right, I believe that the resource drive is similar to what we see on the Windows side as a D: / drive. This is a temporary space for scratches. The disk itself is also VHD and is NOT in the BLOB storage, but actually on the physical server on which the VM is running. For Windows, this is the place where the memory page file is stored in order to maintain latency for accessing the page file as low as possible. They are very categorical due to the fact that this is an uninstalled drive. In your case, this may get stuck if all you have done is disconnect the instance. When the instance turned on again, it was still on the same physical server, so it was assigned the same local resource, so the data you put there will still be there. If the instance has been redistributed, there will be no more data.
3) The disks that you see (OS disk, as well as data disk) are stored in the BLOB storage as a BLOBS page. The cost of storing these disks separately from the charge per hour to actually start the virtual machine. You also pay for storage transactions to access data on these disks as they start. On the pricing page check this quote:
Estimated hours are charged whenever the virtual machine is deployed, regardless of whether it is running or not. Estimated hours do not include Windows Azure storage costs associated with the image running in Windows Azure Virtual Machines. These costs are paid separately.
4) I believe that the resource drive that you see is the equivalent of D: / drive and NOT the local resource space that you pointed to. You specifically pointed to gaining access to local space when working in a cloud service (or previously called a hosting service), so use the Web or Worker role. I am not sure what is also used when using virtual machines. In addition to the page file when using Windows, I believe that this resource space is also used a little when setting up data caching for data disks or the OS, which will reduce the amount of space that you will have. This, in my opinion, is an assumption.
You can also understand caching options and limitations with the OS and data disks. Michael Wusham touches on this in a blog post .