I set up a simple Azure resource group with two servers. As I do not need the servers right now, I stopped and deallocated them.
One of the servers had a specific data disk. This data disk still seems to be alive. It has the status "Unattached" and I can export or delete it in Azure Portal...
Now - am I still being billed for this disc and if so - is there a smart way of somehow stash the disk until I need it again for my VM?
Yes, you are being billed for used storage, no way to "stash" the disk, only way is - deleting it. Or, perhaps, download it and delete it, and reupload at a later date.
Also, another option is to move disk to cold storage, that would save some costs, but Azure Storage is pretty cheap anyway.