Hi, I hope I can help, I did this over the summer when I cleaned up the mess under the intake.
You don't need to have the heater on in the car when removing the drain plug on the engine block. The plug is on the passenger side of the car behind the exhaust headers, it's a little tough to get to but manageable. They recommend a fresh crush washer and you probably want one but if it's only going to be a few weeks I suppose you're likely okay. If you remove the block drain plug you can get most of the old coolant out between the radiator plug and removing the in/outlet hoses from the thermostat. When I did it I think I drained the radiator, then the radiator hoses, and then the block drain plug. Put it all together and filled the system with as much coolant as I could get in (filled the upper radiator hose before connecting it back to the thermostat), then filled the radiator to the cold line, left the radiator cap off, turned the car on, turned the heat and fan all the way up and filled the radiator until it stopped taking coolant. Then bleed the system.
The cars can be a pain to bleed and it helps to elevate the left front of the car as it helps with the process. Also be careful with the bleed screw, you don't need much pressure to close them up, I stripped mine and ended up buying a new radiator. Someone suggested using a quarter to tighten it that way you can't torque it too much, I will always do this in the future.
Good luck, I hope that fresh coolant and a bleed solve your problems.