Coolant box is getting empty from the coolant box and engine noise is more

The AC of my car doesn't work and the fan keeps running loudly. I gave it for service at the authorized service station and the mechanic said that the AC heater core is damaged. The thin aluminum box is broken and the coolant is dripping inside the car hence the fan is running continuously to cool down the engine. The cost for replacement is estimated to be INR 9000. Is there a way we can get it at cheaper price?

There is an issue with the engine cooling system and irregular operation of the radiator fan, which turns on and off inconsistently. Coolant is returning from the radiator, causing the expansion tank to overflow, and sometimes it ejects coolant outside the tank.
In the morning, when starting the car, I noticed a drop in the coolant level inside the radiator. Therefore, I leave the radiator cap open to allow the release of any trapped air while adding coolant until the radiator is completely filled.
However, after driving the car, I noticed air bubbles forming inside the expansion tank, even though the radiator cap is new and in good condition.
Question: What could be the most likely cause of these symptoms?

Every time I park after a few hours starts to be a stain on the floor. I already change the radiator cap.