I want to publish an app witch contains a WebView to my site only and thats the whole app. Like Mobile Web app but comes from the stores. Does app store or Play Store allow apps that have a WebView only to my site?
Yes, you can published an app which contains just a WebView of your own website. Please note that according to Google Play Developer Program Policies, it's not allowed to publish apps that provide a WebView of a website you don't own or administer:
Do not post an app where the primary functionality is to:
Provide a webview of a website not owned or administered by you (unless you have permission from the website owner/administrator to do so)
Reference: http://play.google.com/about/developer-content-policy.html
According to Apple's App Store Review Guidelines, apps which are just web views are not allowed:
4.2 Minimum Functionality
Your app should include features, content, and UI that elevate it beyond a repackaged website. If your app is not particularly useful, unique, or “app-like,” it doesn’t belong on the App Store.
Reference: https://developer.apple.com/app-store/review/guidelines/#functionality