So just to make sure we get off on the right foot. No water in oil and vice versa. Car doesnt leak fluid anywhere and doesnt drop pressure overnight. While car runs for longer periods, it overheats (sorta) and sends water to overflow (classic job of rad cap when the temps go up). Then noticed the fan isn't working. Ok well replace the fan but that doesn't fix the water being sucked back into the motor from the overflow which is what we want. You replaced the radiator cap and cleaned it (cooling system is full of gunk) but what you didnt mention you did or checked is the hose going to the overflow. It sounds like the pressure is pushing whatever shit is in it out so the water can flow to the overflow BUT it appears that MAYBE the gunk is preventing the water from going BACK into the cooling system so maybe take off the hose, clean it, pull out the overflow and clean that too then we can rule out that its a hose/overflow bottle issue. Get back to us when you've sorted that out