Sam, to check the cooling fan is working correctly:
Start the Car
When you are sat in the car press the front screen demist button ( just below the radio on the centre console)
Get out of the car and go around to the front of the bonnet and look through the grill between the headlights.
The large fan behind the grill should be running continuously.
If not then you do have a fan problem. This may not be the only problem but it does need fixing
There are a few ways to do this, all of which involve dismantling the front of the car, reading your posts so far this may not be something you wish to tackle yourself. Seek out active members on here that are close to you and they will be able to guide you to the correct person to complete your repairs and at the best cost