Refrigerant and fan leakage does not work

Hi everyone.
I'm getting desperate about my car because of two main problems. The first is a coolant leak that's been going on for at least a year. The garage replaced the radiator with a new one, but the problem persists. Then they told me to put a new cap on the coolant reservoir (I think it's called the expansion tank), but the problem continues, so I'm not trusting my "trusted" garage anymore. Regarding this issue, I've noticed some dark, greasy strands floating in the coolant in the expansion tank. For now, I'm fixing it by adding coolant, but I'd like to know if this problem could get worse (so I can start saving up in case I eventually have to take it to a garage). And I'd like to know the same thing regarding the second problem with my car: the radiator fan never turns on, even when the temperature reaches the "forbidden" level. Would it be enough to stop the vehicle (and let the engine cool down) each time this overheating occurs (to avoid a garage repair), or do I have to take it to a garage urgently for repairs? Could I fix it myself? Can anyone tell me how?

Greetings to all, and thank you in advance for your help.

Hi mate, I have the same problem with my car, but the fans only turn on when I press the A/C button. Then they work, and of course the temperature drops to 90 or even lower. But if I release the A/C button, it heats up, going into the red zone.
The coolant is also brown, even though I use the green kind.
What I've noticed is that it's not cooling, even though the compressor is engaging.

Let's see if someone can tell us what we can do or what's best to prevent the problem from getting worse.
Regards.

The problem you're having is because the temperature sensor or temperature bulb is damaged, or a relay is faulty, or the fan fuse is blown.
If it's consuming water and you can't see where it's leaking from, it could be due to overheating in the cylinder head, which is being transferred through the engine to the exhaust, making it difficult to see where the water is going.
Check the oil for any traces of water, as this is dangerous and can damage your engine. Good luck.

Thanks for your guidance, but I assume the temperature sensor is the thermostat?
I don't think the fan fuse is the problem in my case because the fans work perfectly when I press the A/C button. I don't know what a relay is.