First drive home from Dealership...

Just drove my 2003 Audi A4 1.8T home today and got a few questions...
 
1. How do you turn on the factory fog lights...
2. What does the "Check button" and the wrench sign mean by the dash? If I press the wrench button, it says "Service!"
3. I drove the car about 30min back to my house and the temperature gauge did not move off the Cold side. Later when I drove it for a short distance it moved to the correct position, is this possibly a problem?
4. Once car is locked, there is a red light that blinks in the car, is this a wana be "fake" alarm?
 
I know these are kind of dumb questions :/ but thank you, as I am a new Audi owner...

ust drove my 2003 Audi A4 1.8T home today and got a few questions...

1. How do you turn on the factory fog lights...

Usually on by default

2. What does the "Check button" and the wrench sign mean by the dash? If I press the wrench button, it says "Service!"

Could mean oil change is due only or any problem on the car. Should not be driven before diagnostics and fix.

3. I drove the car about 30min back to my house and the temperature gauge did not move off the Cold side. Later when I drove it for a short distance it moved to the correct position, is this possibly a problem?
Could mean a faulty CTS or connections; as the CTS supply the ECM with large portion of data - no signal or low usually makes air/fuel mixture very rich.

4. Once car is locked, there is a red light that blinks in the car, is this a wana be "fake" alarm?

Look into your Owners manual!

He, JOnJOn, welcome to Audi ownership (if this is your first one).
As nemohm says, you'll need the owners manual, so you'll know to use the options. On my A6 after I turn on the headlights, pull out the switch to turn on the front fog, and pull it out a second time to turn on the rear fog light. Audis don't have "fake alarm " , it's a real alarm. The temp gauge should show about half way after about 5-7 mins drive. 

Ok, thank you for the replies... Guess this brings up another question, where can I acquire a manual for my car. Wasn't fortunate to have one given to me with the car :/

When I bought my '01 A6 it did not have the owner's manual, I found one on Flea-Bay it's got all the original books in a leather case, fits in the cubby under the steering wheel.
For help with maintenance/repairs I went with Bentley Service Manual, it was $ 100 at Bentley web site but I got it for $ 75 from Amazon.com (this is similar to my post to your other post ;-)  .

Cool, thanks... I am definitely going to look into getting a service manual...