Currently, Azure Functions can only be hosted in an App Service Plan. Each plan requires you to define a specific region, number of VM instances in that region and size of the VMs that must be dedicated to your apps. If your scenario requires the consumption plan, please contact your account manager.
Basic monitoring is available through the functions logs and the monitoring tab in the portal. A richer experience with more analytics options will be available once Azure Application Insights is available.
Azure Functions can be hosted on App Service Virtual Machines.