Stephanie, the dealer installed the relay which cost about $8.00. It is a user-friendly do because it is in one of the fuse boxes in the engine compartment by the battery.
Gas mileage... My 2004 has averaged overall from almost purchase new 41 and a fraction mpg. That's in town, and out of town. What I have noticed is that the summer is great! In warm weather, I can easily get 45+ on the highway if I stay around 65 mph
. In the winter's cold weather, 37 or 38 is "good."
There was no change after replacing the relay.
Hope that helps.