When warmed up, look inside the radiator for turbulence or bubbles when off idle. Turbulence is good, means the water pump is working. Bubbles are bad, most likely a bad head gasket. Check the oil for a grayish color, most likely a water pump seal.
Not necessarily! Check for coolant leaks evidence at the radiator, hoses, tank and motor.
A bad head gasket will pressurize the cooling system with combustion gasses. NOT usually coolant into the cylinder, except when stopped. It will also appear that the overflow is boiling, when it's actually combustion, creating bubbles.
Is there white (or any color) smoke when starting and running?
The BEST way to be sure it's a head gasket,,,, Go to your local emission 'repair' shop, and use their C02 detector in your radiator or overflow tank. It takes a minute, or so, and may be free if you've been there before for service. But slip the shop guy $5 - $10 anyway.
This is kinda out of pocket here but is your fan working? I had a similar scenario that turned out to be a problem with the fan circuit. The fan circuit issue caused it to get too hot while putting through tight woods with women and children, which then blew my head gasket and slightly warped the head