if you just walk in, and plan on using the beach but you're getting dropped off, can you just pay for the car load, and just be there with no cars?

You will be charged but most likely at their motorcycle price. They also don't allow drop off unless you have a ride already inside park. Weather related emergency precautions.

I think you still have to pay, it's part of a state park, if I'm not mistaken

Don't know always in a truck.

You could always call them too

I don't see why they wouldn't allow. But if you go to their fb page, I think you get more answers:)