In the mision no. 3 how close do you have to be go get the stay close check mark in that mission.

It's actually very hard to judge. They adjust their speed if you go really quick so just keep things as fast as you can be staying control. You really can't afford to hit anything and flip over or around. It took me many attempts, but the most difficult bit was about half way around when you get a seemingly pointless cutscene yet you still have control of your car!  If you can get this bit right and not lose sight of Brucie's car you're probably on track.

Early on make sure you go left of the on coming taxi (it always goes the same way) to set you up better for the next turn down the alley. At the end of the alley use the skid marks that the other two leave as a guide for how turn turn without hitting the bridge support or rocks. The rest is just about learning the course.