a restriction somewhere in the cooling system maybe the fan
No, a clogged heater core will not make it overheat. A leaking heater core will.
To make sure the water heater is always supplied and don't run dry, which could cause it to overheat.
First check the truck for coolant leaks, make sure the coolant level is o.k. If it is there could be a blockage in the radiator or hoses if you have no idea what you are doing take it to an automotive repair facility an overheat could cause severe engine damage
The antifreeze level could be low, or the thermostat may need to be replaced, or the antifreeze line might need to be blead to get all the air out, the air in the line will make it overheat.
no but if you try to run the car with the water pump out you could overheat your engine
The thermistat could be bad, check to make sure the fan is kicking on.
No, not an alternator itself. A slipping belt driving the alternator and the water pump could though.
Yes, it could even make it completely ineffective. If it is in a car it can ruin gaskets, seals, or make your car overheat. Which can warp your the pistons in you car.
drive it without coolant
yes
It could, but I'd start by checking the timing. If it's off the car will overheat, and that's easy to adjust. Heater cores are a grade-A pain to replace because you have to take apart the dash to get to them.
Try replacing radiator cap Is cooling fan working? Make sure radiator is not plugged or dirty Check coolant level water pump