What tools do one needs to develop these games?
I'm completely new to game development and very curious about what kind of tools people use to create, for example, this kind of games:
Does Qt have tools for these?
I know Qt has OpenGL module for 3D, but is there anything for 2D?
QML is great for interactive 2D apps :) http://qt.digia.com/Product/qt-quick/
you might consider using V-Play, which is free to download at http://v-play.net.
It is specially made for 2D games and adds gaming-specific components in QML for games like Angry Birds, Fruit Ninja, Cut the Rope, Doodle Jump or even strategy games like Tower Defense. For the latter two there are open-source demo game examples, included in the game engine SDK download. An overview of the demo games is available here: http://doc.v-play.net/beta/vplay-examples.html