That’s because JPanel isn’t set to be focusable in the first place. You have to call JPanel.setFocusable(true) for it to receive focus.
Java2D is slow in either situation. “exclusive graphics card functions”, I don’t know about that one. Those “functions” you seek are low level DirectX/OpenGL functions which are not accessible to you through Java2D nor are they supposed to make anything go “faster”.
I really suggest you stop worrying about tiny performance details like this. As I told you earlier, if your game/app runs at a reasonable framerate, STOP worrying and finish writing your game already! ;D