My low tire pressure light came on a week or so ago (its getting a little cooler in the mornings around here). I checked all the tires, fronts were around 34-35, rears were 31-32 so I put another couple of pounds in them. Restarted the car and haven't had the light turn on since. I haven't pulled out the owners manual, but I'm guessing they have to be over 32.

My car make the same sound for a few seconds then shuts off like yours. Usually right after I get off the highway. I'm sure its just a fan or something, its normal... no worries.