my back up and running lights failed 03amp fuse melted

I replaced the fuse after replacing what I thought was burnt out head light bulbs and running lights after installing new bulbs the problems still was there so went into the electrical and found the fuse melted not blown it also melted some of the fuse box the connector pins still made contact so all the light were restored back to normal!

After putting in a new fuse.

I know have a engine light that is coming on and going off with about every ten starts or so ! It will come on and stay on for a about ten starts and stops then go off for about the same amount of times ! Looked it up in the owners manual it said the cat was bad I now have 62,000 miles on my car! Went back to were I bought the car they pulled the code and said it looks like a bad mas air sensor ? The car runs fine they said it could be running lean which could damage the cat ! I asked if mas air sensor is bad was does it go on and off again after so many starts and stops unable to answer the question !