Radiator fan not coming on?

I come to the conclusion that my radiator fan has not been powering on as it should.

My friend pointed it out to me when we were trying to figure out why the coolant in the reservoir was rising when I would run the car. I hadn't noticed it before but maybe it has been doing that the entire time.

I had to replace my thermostat because it was leaking and stuck open.

My question is, what do I do with the fan to make it work? It powers on if I disconnect the wires and place an external power source to it. I don't see anything wrong with it physically. I don't know what to look for in a relay to determine if that's the problem.

I installed a new temperature sensor. My temperature gauge inside the car always just goes up to the middle. It never passes even when the temperature is over 200°. The car could be overheating, and it would still be in the middle. But the new temperature sensor did not fix that issue, nor did it fix the fan issue. What do I do next?

It also seems that the cooling system might have some pressure in it because the reservoir fills up quite fast as the engine gets hotter. I almost think the coolant isn't circulating at all.