I'm designing a Web-service in Azure. Is it possible to have the actual Azure platform usage costs metered per end-user? And does Azure provide billing services to end-users?
The Windows Azure billing model today focuses on billing the owner of the service account - there are no provisions for a pass-through reselling type of billing.
The recommended model for selling applications and services running on Windows Azure today is to set up a new Windows Azure account for/with your client and deploy your Windows Azure service or web application into the client's Windows Azure account. The client pays Windows Azure directly for time, storage, and bandwidth they use, and the client pays you separately for developing or maintaining the application.
This model is workable if your client is a business that wants to use your Azure software to support thousands of their customers - each client business would have their own Azure account. This model does not work if your software is a single user application such as a personal tax package or solitaire card game that you are selling to individual end users.