Is the coolant resevoir for excess hot water/antifreeze? Does the radiator take coolant out of the resevoir?

 

Yes & yes.

As the engine heats up, the coolant expands (which is why the coolant level looks higher in the radiator if the engine has been running for a few minutes, than when it was cold).
Excess is released by the radiator cap into the reservoir.

Then as the engine cools overnight, the coolant is drawn back into the radiator.

The specified "1.5 inches below the filler neck" level, allows for the normal expansion & the overflow tank looks after the rest.

 

So it is important to keep antifreeze/water in the resevoir. I recently bought the truck noticed that it's empty. That might explain why the engine runs a little hot being that the radiator is low on coolant? I checked for leaks and hoses, filled everything to proper levels and will see what happens. Thanks

 

Not exactly correct. Your are correct, the coolant expands and contracts as it heats and cools. On the old cars and trucks without a reservoir tank, you did need to leave a air space in the top of the radiator for expansion. You could fill the radiator up, and when it got hot, let it puke out the excess on the ground, and it would find the correct level itself, or like you said you could guess and leave some air space in the top yourself.

On the newer cars and trucks like ours, they decided they wanted the radiator full to the top at all times. So they invented the special recovery radiator cap, and installed the reservoir or "storage" tank. You can then fill the radiator to the top, when it expands it flows out to the tank, and then when it cools and contracts, the special cap lets it suck the fluid back out of the tank and into the radiator, and thus the radiator stays full to the top. If you notice, the hose that goes into the tank goes all the way to the bottom so it can be submerged in the coolant and draw it back into the radiator without sucking air.

 

It is important to keep coolant in the overflow container so the system can stay full. But, just because there isn't any in there doesn't mean the engine will run hot. Anyway, fill it up to the appropriate mark and find out.