Yes some coils need a resistor. It sounds like you will have to clean and maybe replace some stuff. If your pickup has turn signals they were added later and evidently used the parking lights in the head lights. In the rear they use the stop lights. So both park lights will be hooked into the turn signal switch.

It will start and run with no generator or alternator or battery charger if the battery is good and charged. Lights will work as well as all other electrical equipment. It will work until the battery is dead then you will have to charge it. Having the charging system working keeps the battery from going dead. With a generator you can push start a standard transmission car with a totally dead battery or no battery. Alternators need an exciter current to work. Some might make their own but not most. When using your wire diagram just focus on one circuit at a time and trace it out. Don't try to take it all in at once. Have it enlarged if you can't see it well. The ones in most manuals are too small. Just trust what they did and don't second guess them. They were engineers and usually found difficult ways to do simple things just because they could. The turn signals on my son's '54 Studebaker drove me nuts. I rewired the whole car an threw away ALL of the stock wiring. The only problem is that I burned up a headlight switch because I didn't put in a relay. It works fine now.

"I wonder if God created man because he was disappointed in the monkey?" Mark Twain