Is the deployment scenario mentioned correct (Azure Web Site vs Azure Cloud Service)?
Azure Website and Azure Cloud Service are two (of the three) ways in which you can deploy your code in Windows Azure. Azure Cloud Service is Platform as a Service (PaaS) offering from Windows Azure and you can think of Azure Website as a specialized PaaS offering. Please see this thread on difference between the two: What is the difference between an Azure Web Site and an Azure Web Role.
Can I create a local SQL Server database for development purposes and then deploy to Azure SQL Database (doesn't matter if I only create schema without any data on Azure later)
Generally speaking yes. There are some differences between Windows Azure SQL Database and Local SQL Server and as long as your database does not include those unsupported features (like CLR data types for example), you should be fine. Please see this link for more details: http://msdn.microsoft.com/en-us/library/ee336281.aspx.
How do I develop for Azure Tables locally? How do I develop for Azure Blob storage locally?
You would need to use Windows Azure SDK for that purpose. When you install Windows Azure SDK it also installs a Storage Emulator. Storage emulator has support for Azure Tables and Blob Storage. Current version of SDK is 2.2 which you can download/install from here: http://www.windowsazure.com/en-us/downloads/. Once you install the SDK you will see options to manage storage emulator in Visual Studio Server Explorer.
Note: Storage emulator which is included in version 2.2 does not support latest version of storage client library and for that you would need to install storage emulator 2.2.1 which is in preview currently. You can read more about it here: http://blogs.msdn.com/b/windowsazurestorage/archive/2014/01/27/windows-azure-storage-emulator-2-2-1-preview-release-with-support-for-2013-08-15-version.aspx.