Q: I understand that there's a monthly cost to replicate a virtual machine to Azure using Azure Site Recovery. Am I also charged for compute resources?
A: Azure Site Recovery has a monthly charge for each virtual machine that's protected by Azure. During normal protection, there's no virtual machine running in Azure; only the storage of the virtual machine is replicated to Azure storage. In the event of an actual disaster, a virtual machine is provisioned that's connected to the replicated storage—which is the time that compute charges would be incurred. However, there are no compute charges during the normal replication of a virtual machine.
You can find details of Azure Site Recovery pricing on the Azure Site Recovery Pricing page. Note that each protected virtual machine includes 100GB of georeplicated Azure storage for the actual storage of the replicated virtual machine virtual disks.