I have an App Service in my Azure account which I deployed with Visual Studio Publish wizard. Is it possible to restore the deployed solution locally (in Visual Studio) from
When you publish an app to an App Service (web app), just your code is published, not the Visual Studio project / solution files. So no, unless you somehow forcibly packaged (or maybe ftp'd) a copy of your solution files, they won't be available for download.
It's fairly trivial to pull the app down to a local machine though, since Web App has built-in ftp. Just don't count on being able to retrieve source code for languages such as c# and Java (since usually just the dll/jar files are published).