Which engine to use ?

You don't need an engine for any of those games at all, you could just build the games without having to worry. When you start getting into 2d graphics you could just use something like SFML.

If you are going to make easy games you dont need any engines.You can pick up an library and start playing around with it

If you ask me you can use Unity, It is a 3d game engine but sill you can do 2d games in that I have one video collection on how to make 2d games in unity, i can give it to you if you want it, other than that if you still don't want 3d game engine, then you can program games yourself with any programming languages, i have made a shuffle game when i started programming, i can give you the download link for he game if you want it too. But my advice i use a 3d engine to do your 2d game so it looks more nice.

What if one was to make an extensive 2d game, would you recommend an engine for that? Like if I were to make a bullet hell space shooter game.

I would use SFML:
http://www.sfml-dev.org/

You can also consider Allegro, SDL and Clanlib. Out of these I have only used SFML, and it was a pleasant experience (~2 years ago). For a bullet hell shooter, a more extensive engine than these four would not really help you.