Hello and welcome to JustAnswer!
If the power steering fluid is full then you've very likely got a bad power steering pump. As you probably know your truck has a hydroboost brake system, which runs off power steering pump pressure instead of vacuum. This is why you've lost both power steering and power brakes at the same time.
The only way to know if the pump is the problem for sure or not would be to check the pressure leaving the pump, but it's very likely the pump. It's not unheard of. If it was something like a restriction in the system I would expect some pump noise and at least partial assist from the system.
No, you wouldn't have to take the radiator out. The power steering pump is mounted to the back of the vacuum pump, which is mounted to the back of the timing cover on the left side under the injector pump area. To remove the power steering pump you would remove the return line, remove the pressure line, and then remove the 15mm nuts that hold the pump to the vacuum pump. You will then slide it to the rear and remove it.
You'll notice that the power steering pump is driven by the vacuum pump. If you look into the end of the vacuum pump and look at the power steering pump shaft you'll see how they engage each other. You have to be very careful when putting it back together and be certain that it's lined up. You can actually draw the pump into place without it being lined up, and the pump won't work. To stop this from happening the service information has you removing the power steering and vacuum pumps together and separating them on the bench, but I personally prefer to just remove the power steering pump.
Either way you wouldn't need any special tools. A 15mm starter wrench and/or 15mm swivel socket will be helpful, and an 18mm line wrench is best used to remove the power steering line, but no actual special tools are needed.
If your cruise control works, four wheel drive works, and the heat will switch modes from floor, vent, and defrost, then the vacuum pump is working normally.
Basically yes. The fluid reservoir is on the back of the power steering pump and is actually part of the pump, serviced with it.