1- The radiator cap serves two purposes. It keeps the fluid in the radiator and it regulates the amount of pressure that can build in the cooling system. The coolant expands when heated and creates this pressure. The cap has a valve that opens when the pressure reaches the value indicated on the cap, and the coolant flows into the coolant reservoir. As the engine cools and the coolant shrinks a vacuum is created in the system that opens another valve in the cap and allows the coolant to flow from the reservoir back into the radiator.
2- I too reached Chakwal yesterday from Lahore and believe me no one bothered to check for fog lights. But as a precuation I pasted yellow cellophane paper on my headlights. You can do this too if you like.
I started journey at 1:30 and reached Chakwal at 6PM easily. No fog encountered.