The fan running after you shut off the car is completely normal. Mine does it all the time (desert heat probably makes mine run more than yours). Every small car I've owned has done that, since my 78 VW Rabbit. Many modern cars use electric cooling fans now instead of linking them to the engine anymore. This is one of the reasons they insist that you disconnect the battery before doing any work on the car! That fan can come on unexpectedly at any time.

As for tires, I replaced my OEM Dunlops with Michelin Harmony from Discount Tire. I took a definite hit in MPG, between 5-10%. It's extremely difficult to choose tires for these cars. I could have gotten the Dunlops again, many people hate them but they worked great for me and lasted 50% longer than their warranty to 60k miles. But they were a special order tire and the same price as the Michelins. I really wanted a standard stock tire so I wouldn't get stranded somewhere with a broken freakish irreplaceable tire. I tried to research rolling resistance and such, but there's very little data out there. The Green Seal report everybody totes is so old that hardly any of those tires are available anymore, and consumer reports claims to have rated tires on that criteria but reading their ratings didn't really help much either. If you're getting good mileage and performance out of your tires now, I strongly recommend leaving them on there until you have to replace them. No sense spoiling a good thing, keep it going while you can.