There is no need to pre-warm your car for 5 minutes in the morning before you leave. This just wastes gas and can actually harm the car. You can idle for about 10-60 seconds, and then drive. Once the car has come-up to normal op temp (engine temp and tranny loosens up- oil temps quickly mirror engine temps) you can increase RPMs over the 3,000-4,000 range. This would be much improved to sitting for 5 minutes.
As for your fans running after the car shuts off...I don't know what is considered normal, but I am sure you will get your answer here soon.
