Car over heated due to lack of antifreeze?

So, it's a used car from Byrider and it decided to tell me engine overheated idle and it's on the car off. Now my uncle decided to wet the radiator with a water hose from the outside to try to cool the car down and then proceeded to put the hose in the new bottle of antifreeze that was Dexron 50/50 disregarding. The label says do not add water. Put it in the car with a car running and then put the water hose in it in the reservoir. After that we waited for the car to cool down entirely for about 2-3 hours, came back to find out that the argument of the 50/50 meeting water the bottle said do not add water. So, I unplugged the radiator drain some of the liquid inside out which came out almost completely. Antifreeze everybody put the hose in the reservoir it was still too hot and came out the back of the reservoir the Overflow so the way the antifreeze look the Dexron looked coming out of the bottom of the drain hole it was mostly dextron. So, I plugged it back up and moved over to the reservoir on the hook the reservoir and poured out the water down dextron in a bucket since the car is completely cold at this point. I pour all the extra on into the reservoir and leave the radiator cap tight fill up the reservoir and then turn the car on, car is running just fine idling just fine. Then we take it around the block but it's time we only got three streets down in the neighborhood and back to the house the gauges red that the car was in the middle temperature which is normal. Opening the hood there was slight smoke coming from the radiator like very slight only can see in a certain angle. When I go to take off the radiator cap it spewed out indicating to me that it's too hot for only going three streets up and back. So, then I go and look and radiator cap once it's cool and there's nothing that I can see and there's that slight smoke coming from inside radiator cap. So, I take a funnel put it in the radiator cap entrance turn the car on turn the heat on nothing happens it's still reading normal turn on the heater and it starts to bubble if I pour the Dexron in to the radiator cap hole while the car is running for the car back off put the radiator cap back on turn the car back on but the car sitting idling it reads normal, but the hose from the radiator and radiator cap engine is now stiffening and the fans do not turn on. So, I have to now jump the fans in order to get my vehicle home correct without overheating. Is it the fans or the thermostat that's the problem?