Bmw 318I Convertible Coolant Going Down And Rad Fan On All The Time

hi im new to this site hope im not doing anything wrong

i have a bmw 318i convertible iv just brought the car and iv noticed that everytime i switch the ignition on before starting the rad fan comes on straight away and stays on intill you switch everything off, does anyone no y this is? i think that the fan has been set up to run all the time but could be wrong, and i did notice the the temp sensor i think its that its on the top left side of the rad it was not plugged in but it makes no difference if its plugged in or not so i donno. and the person i brought the car of said the coolant sometime gos down a little back he said he just opens the bleed screw on the top of the rad and the coolant come up i dont no ys this is, but all of this the engine temp sits at normal all the time when warm car drive fine as it should with 79,000 miles on the clock , i will say the car has had a new stat no water in the oil nothing out the back all pipes are warm so i dont think its head gasket or head, but the 2 problems are getting to me i just wont to sort it and any help on fixing the problems would be very greatful thanks. matt