I am new to Stack Apps, so need help in getting started:
A tutorial on Stack Apps.
What languages I need to learn to get started with Stack Apps.
List of apps in Stack Apps.
This is pretty much all on StackApps itself. There isn't exactly a tutorial, but there's documentation, a Hello World app, and a Sample app you can read through (the apps use the 1.1 API though). You can use any language, as long as it's capable of communicating with the API interface; if you want to use a library you'll need to choose one of the languages that has one. The list of apps is available on the homepage, in the apps tab