Q: Rough idle, no power in low gears , hesitation and very poor gas mileage with p0300, p0420 and p0455 codes

Hi There, These codes are more than likely related to each other and causing the misfiring that is a result of code P0300. Code P0420 relates to the catalyst system being inefficient, which is usually the cause of a catalytic converter failing or an oxygen sensor malfunctioning. Code P0455 relates to an EVAP system leak, which means that the vent control valve is likely damaged or not working properly. Your car has a small purge valve with a purge solenoid in the Evaporative Emissions system that controls the venting of fumes from the fuel tank as these fumes build up inside, particularly when you are refueling the car with gas. The EVAP system prevents fuel vapors from the fuel tank from escaping into the atmosphere. The EVAP system collects and temporarily stores the fuel vapors in the charcoal canister. The charcoal canister is filled with activated carbon pellets that can absorb the fuel vapors. When the engine is running, the fuel vapors are purged from the canister and burned in the engine. The vent control valve (solenoid) controls the flow of outside air in and out of the charcoal canister. The vent valve is controlled by the engine computer (PCM). Normally the vent valve is open. It closes when the engine computer tests the EVAP system for leaks. If a leak in the EVAP system is detected, the Check Engine light will illuminate on the dash and the trouble code related to the problem will be stored in the engine computer. When an air leak is present in the EVAP system, the MAP sensor will not be able to determine the air density, and the MAF sensor will not be able to determine the volume of air, entering the engine correctly. This will lead to an over fueling situation or an under fueling situation depending on the size of the air leak and engine operating speeds and load. This may eventually lead to catalytic converter problems as well as misfiring problems. I would recommend having an expert from Your Mechanic come to your location to diagnose and inspect your vehicle.