My Nexstar came with the lines hooked up wrong.

I think the fuel getting sucked back into the tank is pretty normal. You get pressure from the exhaust into the tank, which forces fuel out of the tank toward the engine. When you shut it down, pressure wants to escape, and since you have a good seal in your engine, it escapes out the muffler, which I imagine is causing a low pressure zone, and therefore everything is getting sucked that way.

I agree that it sounds like you're running lean. Do you have the right fuel (18% lubrication at least)? Do you know about the pinch test? Pinch the line to the carb for a fraction of a second when the engine is running full tilt, and you should hear a spike (increase) in RPM's. If you don't, you're too lean and need to turn the needle valve counter clockwise.

Good luck.