RE: Dynam Peaks Pitts servo will not center and ESC issues
Re: Beeps
The short beeps are because the ESC is not seeing the throttle go to zero.
Re: Servo
If the servo is not centering with the linkages disconnected, then it is definitely a bad servo.
Given that you want a stronger servo for the rudder anyway, just obtain any similarly sized, but hopefully stronger servo to replace it.