The heater core does not care if the fan is on or not, unless your truck came with factory AC the heater water flow is controlled by a cable on the dash, it leaks by enough anyway so that is a non issue.
Make sure to use spec fluids, DOT 5 SILICONE brake fluid ONLY, not 5.1 and yes it is very expensive.
Use green "old school" coolant, you just fill it to the line on the reservoir, could not be simpler.
There are many you-tube vids on bleeding the brakes.
Make sure all the brake bleeding screws are in place and can be opened before starting.
If your truck was truly headed to the scrap heap I would expect to find drain plugs missing and maybe even a hole or two in the trans pan and or fuel tank.
INSPECT EVERYTHING, hoses, clamps fittings, wire connections, extra time here will save you money in the long run, remove the check valves located in front of the fuel tank, do not forget you have geared hubs behind the wheels that need servicing.
Do NOT push as hard as you can on the brake pedal while bleeding or any other time while the engine is running, you can possibly blow the seals in the hydo-boost.
The maintenance, operator and parts TMs are an invaluable resource, take the time to read and understand them before starting on your truck.
Nobody likes homework but it will give you a MUCH better understanding of your truck, if you are not willing to spend time with the TMs then it would be far better to have a pro familiar with the HMMWV do your work as it is a very different animal.
Here is alink to the TM sticky, the first link will take you to a site that has all the TMs you will need to start.
https://www.steelsoldiers.com/threads/hmmwv-technical-manuals-if-you-need-it-its-here.189594/
