A mechanic worked on the compressor and he flushed out the coolant system and only filled it up with water.
Afterwards, the coolant water keep drying up and I had to top it up with 2 liters of water every day and have tried to finds out the war leakage but no where to be found. I then decided to add 1 liter of coolant and the water keeps drying up after.
What can be the cause and what can I do to prevent engine damage? Should I add more coolant?
I would remove the radiator cap, start the vehicle, and look for bubbles and/or foam.
It's a sealed system (or at least it should be) and 2 liters/day is far too much loss. It has to be going somewhere.
If it's not dripping on the ground, it's going out the tailpipe. In the morning, water vapor is discharged and looks like steam - but this isn't much of a concern.
Better you should smell the vapor (but don't get hooked; just some sniffs) and see if anything smells oddly sweet.
Also, if there's a film on the inside of your windshield, you may have a heater core issue... But this I doubt, as 2 liters/day would be a cloud that prevents you from driving.
Again, operate the car stationary at idle over some clean cardboard under the engine area until it is plenty hot. Check the cardboard for drips. Without anything visible leaking, your next step is a compression test. Unfortunately a bad result here will be very expensive.
Also, as @Zaid mentioned, a bad radiator cap could cause this - although you should be able to smell this as well. You can test or have the cap tested, but they are so inexpensive it may be worth just replacing to see if that cures the issue.
Low coolant boiling temperature is likely one of two things:
Low boiling point
This is remedied by adding anti-freeze which has the effect of raising boiling temperature.
Low system pressure
The cooling system is operating at below-normal pressure. A bad radiator/expansion-tank cap is a prime suspect in such circumstances.
