bad test readings/ water changes?

As many as it takes to keep the Ammonia and Nitrites at 0.

First, throw out all the old filter medium, floss and charcoal, because it's probably growing BAD anaerobic bacteria after the power outage. Start with new floss and new charcoal. Don't want to shock the fish with too much of water change, so just change 2gallons a day until ammonia back to zero -- make sure you're siphoning out from the gravel -- and get out lots of fish poops and uneaten food. The glass, gravel, ornaments -- all surfaces will likely still have enough nitrifying bacteria to rapidly get things under control -- so don't worry too much about it. Most fish can tolerate a little ammonia for a few days.

Use Prime or other ammonia locking conditioner, Prime works on nitrite too. But keep up the water changing. the API test will still show ammonia but it will be in the less toxic ammonium form. I also is good your pH is below 7, that helps with ammonia too. Good luck