How to fill up the coolant on my audi a3 car - 2006 Audi A3

https://www.youtube.com/watch?v=5C2HtiV8DK0

Step 2 - Check transmission fluid Place the drain pan under the transmission's drain plug, then loosen the plug with a 14mm Alllen wrench. If the fluid is up to temperature and at the right level, only a very small amount will drip out, but if none comes out at all, chances are you are low.
https://www.audiworld.com/how-tos/a/audi-a3-how-to-check-and-change-s-tronic-automatic-transmission-fluid-420892

This sensor should be located in the thermostat housing.

GL.

images for Front wiper fuse on audi A3 2006 please

On this website you find fuse box diagram and description for Audi A3

Audi A3 2008 fuse box diagram

Haven't heard of a relay switch for coolant fan. You must be talking about thermoswitch which starts your coolant fan when coolant reaches a certain temperature. Normally it is fitted on the radiator itself

You're going to need to visually inspect for leaks and if no external leaks are evident I suspect your head gaskets are leaking again - check oil for coolant in oil - it will look milky

Cooling system capacity for a 2001 Audi A3 1.9 TDI is 5,0 litres.

try taking off the gas cap and then retighten it.may have a vacume lock.make sure gas cap is tight.

In my experience with Audis, after any job requiring changing/draining the coolant the car ideally needs to be driven. With the coolant topped up to max drive the car, keep the revs up and shake the car with steering and over bumps where possible. Whatever you do make sure you take at least 2 litres of water/coolant with you, as as soon as the air lock goes, the level drops a lot and quickly. Also keep an eye on the temp gauge and avoid letting it go much over 90 degrees (over 90 on the gauge usually means its well into the hundreds) When you get consistant hot air through the heater, at idle, the level should of settled. If this doesnt work you may have thermostat issues or a blockage. Good luck, let me know how you get on.

ON ALL A4 MODELS AND I THINK THE A3 , THE ENGINE COOLANT TEMPERATURE SENSOR IS LOCATED AT THE REAR OF THE CYLINDER HEAD,WHILST ON SOME ENGINES, A SECOND SENSOR IS FITTED TO THE RADIATOR OUTLET PIPE...HOPE I WAS OF SOME HELP TO YOU....