I am getting this indicator lamp "( O )" on my AUDI A4 year 2005 since two days ago. Can you tell me what is it?

That's too bad. Unfortunately the repair shop is probably right. Take it to a couple other shops for a quote just to be sure.

It's an yellow warning indicator lamp. It lights when brake pads are weared. Now it's time to replace the used brake pads!

check to see if an aftermarket cat was put on and on this model it has to have a stock one

It's an yellow warning indicator lamp. It lights when brake pads are weared. Now it's time to replace used brake pads!

Audi 1.9 TDI and 2.0 TDI engines with pump-nozzle injection system, (year 2005 included), don't have permission to run with Bio fuel !!!
First you must replace fuel filter, interflow a quality Diesel additive (for 60 liters Diesel fuel dosage) fill up tank with Diesel fuel and run at least 300 km on highway at 3000-3500 rpm in 4-th gear.
I recommend you Foerch Diesel Reiniger System additive! I use this additive from 3 years ago and is certified on Audi TDI engines!

Check the coolant temperature sensor housing in back of the engine. This is made out of plastic on some model years A4 and eventually leaks coolant.

I too have the same problem on my 2005 1.8t B6. I noticed a hole in the breather hose coming off the valve cover that runs to another port under the intake manifold. I have the hoses on order and should be here on Wednesday. I'll post again if that fixes my problem.

i have a transmition problem on a 2003 audi a4 1.8t whit 44000klm.
audi is changing transmition at no cost but have to paye for labor

First tell me what code did you get from the obd2 tester. your so called mechanic should have told you. you can do the same erasing by disconecting the batery for half an hour.
Is the car running good or bad and how is your mialege and is it very hot at the catalictic converter, probably it is your O2 sensor going bad , check what codes you are getting first, Vitally