The commode makes a sound like it has been flushed and refilling when it has not been flushed at all. Is there a possible leak between the tank and the bowl? Is a seal not closing properly? Does the wax ring under the commode need to be replaced or just a whole new commode?
Do not make the job more difficult than it really is. The problem is in the tank, not the toilet or the wax ring. Either your flapper is worn out and needs to be replaced, or the little rubber tube from the fill valve is inserted too far down into the overflow pipe. It should be above the pipe or inserted no more than one inch down into the overflow pipe.