Put a Canvas in the JFrame (or Frame) and get the BufferStrategy from that.
Thanks, that fixed one of my problems.
The problem I have left it's the re-size one. The canvas still render more when someone resize the JFrame. But I want it to stretch. The reason why I want stretch, rather than render more. is because it would be much easier to do HUD's since I know the game always going to be a set resolution, instead of a width and height that could be anything.
I could just do it with a BufferedImage. But I want to see if it's any better alternative first.
Edit: I couldn't fix it with a BufferedImage, I tried and the frame rate went down from 1300 fps, to 150 fps.