I recently had a problem with the electrical connection on top of the injectors, my car would chug and then i push down on one of the tops of the connections and it 'clicked' and my car doesn't chug 'as-bad' anymore. I can also move the injectors from side-to-side (they kinda turn left to right) while installed. Are they supposed to move at all?

 

If you look at the connector you will see a wire clip that holds the connector onto the injector. Make sure the connector is pressed down so that the clip engages the injector properly.

Don't worry about the injector "looseness". They have an O-ring at top and at the bottom to seal at the fuel rail and at the intake base. So there is normally some rotation possible. So long as no fuel is seeping you have no problem there.