Your headlights are coming on because our cars have daytime running lights (DRLs). They come on at reduced voltage anytime the engine is running. If you don't want them on while the car warms up, you can set the parking brake before starting the car and they won't come on until the parking brake is released.
If you want to disable them completely, there's a plug you have to pull in the dash. Open up the panel on the side of the driver's side of the dash, and you'll see a module with a huge heat sink (lots of metal fins). Pull the plug from this module, and the DRLs will be disabled.
Sorry, but I can't help you with the speedometer. I'm sure someone who can will post soon.
