The first thing you need to do is fix the fan problem, as no matter if the engine has no fault other than fan it will still overheat if idling long enough.
Is your heater ok ?, if it is this shows the water pump is circulating water, leaving the stat as the most likely culprit, a cap seal can do it but would have to be seriously knackered or missing, when you twist the cap do you get a hiss, if you do it's holding pressure.
You can check the gauge by earthing out the gauge sender lead onto the engine and it should show max, seems like you may have more than 1 problem.
tabetha