I bought the Hawk X 250 recently. Carburated. I'm glad I didn't get the fuel injection. Mine is counterbalanced. Runs smooth with stock carb. Very low vibration. No problems. Make sure all of your electrical connectors are tight especially for the ECM. That can cause issues.
Good comparison between the stock and your new exhaust. I'm sure having fixed that cracked header pipe helped out some too. Ugh sorry to hear about the electrical issues. Those are hidden gremlins 😕
Its normal to lose a little torque when you replace the full stock exhaust without a tune. Unfortunately, the Hawk is not known to be a fire breathing high rpm machine. Since you replaced the o2 sensor, check the fuel filter, and clean the carburetor. Better yet, upgrade to a bigger carb if thats the model you have. (or try an additive to clean the fuel injector if its fuel injected) Good luck and ride safe brother.
Like you said maybe the kill switch is bad. And I would guess maybe the o2 sensor is bad. That would keep it from running well. I had a kill switch go bad on a ride I just bypassed it. Good luck with it. 👍