Can I use nginX+Webkit+PHP+SQLite to create Mac Appstore applications?

There are two approaches for this:

1) With building a full blown application in just PHP, there is a framework called miniPHP. It's the only thing I could find for OS X, other than WinBinder (windows only).

2) Build a web based application and embed it in a WebView. The OS X GUI would be in Objective C, but the meat of the application would be on the server.

I personally feel option #1 is a bad idea because PHP isn't designed to run as an instance application. It's better used for web applications or command line scripts.

Option #2 is your best option. I believe the WebView has bindings with JavaScript to make calls to/from the GUI application. I personally haven't used WebView, so I'm not sure how that works. I mostly develop on iOS, and the UIWebView is limited by comparison.

Shortly, you can't.

PHP is a back-end language. Though you can use the Webkit engine in OSX to run your app, the GUI of your app should be write in Javascript and HTML. You can search google with "HTML5 native app" to get more information.

As for Nginx, it is a server program. It serves for server but not client. Anyone who wants to build an app in Mac Store or Google Play or whatever should not involve Nginx.

SQLite can be helpful in native app development, I think you could use SQLite with some form of API that the framework you use providing.

To get more info, see PhoneGap and Node-webkit, they could help you assuming you are a web developer. And if you plan to develop on OSX, the recommend way is Objective-c Language and Cocoa Framework and Xcode IDE.