Ok, great. So, let's start with your question- After clearing the codes (or replacing the battery) this resets the on-board computer and you then need to do a "Drive Cycle". This is roughly 50-75 miles of combined city and highway driving. HOWEVER, is the codes were not addressed or were not fixed properly, before you get the Drive Cycle finished, the Check Engine Light WILL return, and you'll be right back in this same spot. So you'll need to address the codes first... THEN do the drive cycle... THEN return for re-inspection.
The P0031 is a fairly common problem. It points to a problem with the Upstream Oxygen Sensor. Very common wear and tear fail item. If the wire harness and connector look good, replacement is usually the answer.
The P0455 is a large EVAP Leak. Very commonly this is a faulty Fuel Cap. Make sure it is tight and seated correctly. Check the underside of the fuel cap for any cracks or signs of defects that may keep the cap from sealing correctly. If there are any doubts about the inspection of the cap, replace it. Keep in mind, you will need a cap that meets OE Specs. Those "universal" or "locking" fuel caps sold at after market parts stores do not meet OE specs, and will not seal the system correctly. If you are sure the cap is good, then an EVAP System "smoke" test will be needed. This is where a machine forces smoke through the system and any leaks can then be easily found and repaired.
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