[Christ]

Swap your cap for a new(ish) one.

Test the temperature (with your hand) of the radiator hoses and the heater core hoses. If one of the radiator hoses is cold(ish) while the other one is hot, the thermostat has not opened. If the engine has been warm for some time, the thermostat is stuck shut. You can test this by putting it in a pan of boiling water. As the water in the pan reaches the stat's pop temp, it will quickly open (think "boing!"). If that happens, let it cool, and reinstall it. There is a chance it could have been installed backward previously. If the issue continues, at least you've eliminated the stat from the loop.

The engine will smoke until the rings seat. When it's at higher RPM, the smoke stops because you've burned it off the piston top and exposed walls.

The boiling coolant means you don't have proper pressure in the system somewhere. While the engine is cold, remove the radiator cap and start the engine. Check for bubbles in the radiator. If there are any, replace the head gasket, as it hasn't sealed properly. (You could also get away with using head gasket sealer, if you were so inclined.)

When the coolant is under pressure, it should not boil at all. If the engine isn't overheating, the cap should not open (the pressure in the radiator shouldn't reach high enough to blow the cap) and release coolant into the overflow tank. My truck does the same thing, and never sucks it back in, so I just run the coolant a bit low, and it's fine now.

You should not fill the coolant to the top of the filler neck... That's too full, and there will be no expansion room in the system for added pressure. If you keep adding back coolant when you see it blow off like that, it's going to keep blowing off as the pressure rises. Once it cools back down, the radiator will look like it's not quite full, which is normal. If the overflow tank inlet hose is not immersed in coolant (at the bottom of the tank) the radiator will not be able to pull in the dispersed coolant as it cools down, either. This is key to the overflow working properly, if you intend for it to do so.