How can I search for an App in the ITunes App Store in a webbrowser
iTunes has a search API as documented here, you don't need to use Google. To search for apps only, set entity to software. If you want to call this from your website via JavaScript, you'll probably also need to set callback to something appropriate. 

Here is an example search URL which will return results for apps with "myApp" https://itunes.apple.com/search?term=MyApp&amp;entity=software