Is there a spigot where we'd be able to fill our camper's water tank once we get there? Would prefer to travel without the extra water weight.

None of them have a hose hook-up. So filling an RV would be hard to do

There are definitely multiple water sources. I'm not positive what those connections there may be, but plenty of fresh running water you have access to. But no sinks or water in the toilets / restrooms.

Not sure as I've only tent camped there, but my friend has an RV trailer and camps there often so I would imagine so. Check this link for more info https://www.recreation.gov/camping/campgrounds/119140