I don't think you said what year car you have.
Earlier cars had a hose running from that nipple under the cap, then along the top of the radiator, down the side and then it ends near the bottom and spills onto the ground. There should be a metal clip on the radiator to hold the hose on the side.
Then in the early 70's, cars started using a closed system with an overflow bottle. You could convert to that pretty easily by getting a new raduator cap, say for a 73 Dart, and a plastic overflow bottle. Expansion forces the excess into the bottle which then gets drawn back into the radiator as it cools.
Go to a large chain auto parts store and "rent" a cooling system checker for free. You can pump up the cooling system at the radiator cap fitting and see if there are any leaks. It should hold 16 psi steadily without dropping. It can also be used to check caps.
It sounds like you are aware that coolant will raise the boiling temperature. Of course do not remove a cap from a hot system. That lever style cap is supposed to relieve pressure but is not Mopar correct.
