I am using a CG Machine, and balancing my airplane. But, how do I know when it's level? What point of reference on the plane do I use? Is the stabilizer a good point of reference for level? The CG machine included a very light weight level and suggested putting on the Stab. Are stabilizers always supposed to be a refrence for level?

Your getting way to particular here. If it looks level then that's close enough. I usually balance so the nose is down just a tad. This really isn't rocket science. And to answer your question about the horiz stab - yes that would be a good reference for level. I wouldn't be to wild about adding the weight of even a light weight level to the stab while I was checking for balance. I think you'd be better off just eye balling it.

With kits and plans built planes there is a line going through the fuse on the plans called the datum line, that is the true center for level. Most stabs are set at zero incidence so it's another good spot to put the little bubble level. I have one I use that almost weighs nothing but they can make a bit of difference. You should start with a slightly nose heavy plane anyway so the little added weight shouldn't be any big problem.

Even if you think its perfectly level on the Cg "machine"...One you put it in the air it might still need slight adjustment to fly how you like it. If It looks level...you should be good. Its better to see it pointing down slightly than pointing up. Its easier to fly and adjust from there.

Don't worry about "level" so much. The CG machine will show you if the plane's nose or tail are heavy. With a low wing plane balance it up side down and a high wing balance it with the plane right side up. If the tail or nose drops then it is heavy. This is after you have by hand made the plane level on the CG machine and then let it move on its own on the balance machine. Reposition your battery as a first choice to balance the plane. If moving the battery doesn't give you the desired CG, then some weight(lead tire weights, BBs in epoxy, fishing weights, whatever that can be firmly held in place) can be added forward or aft to make the plane balance near the CG point you want.