As a furloughed National Park Service Ranger a few answers for you.
One, all National Park Service sites, including World War II Memorial, were shut down. Currently, the Honor Flight vets have been let in by calling it a First Amendment activity, which I think was pretty quick thinking on someone’s part. Other visitors have been kept out.
Two, about 3,200 NPS employees were not furloughed. Those people are currently working, but not being paid now. 2/3 of those are Law Enforcement, EMS, and fire. This includes the Park Police who cover the DC area parks. So yes, there are armed Rangers at the World War II Memorial, as well as other NPS sites. These are not additional Law Enforcement rangers on duty but actually a reduced number of the normal amount due to the shutdown. However, since they are standing at the gates turning people away they are much more visible than usual.
Three, as for websites, at least in the case of the NPS this one I know exactly what happened since I manage two sites. We didn’t do anything to our individual park websites, instead a single master switch was thrown and all are redirecting to the main DOI website. This was done so that A: there was a single message going out, not 400+ versions of the message, and B: prevents visitors from misunderstanding out status and trying to ask questions or make reservations on-line where there is no one to reply to them.
Four, as for privately run campgrounds being closed. Those campgrounds are concessions within the park boundaries - just like many restaurants, hotels, shops, and recreational vendors. Their contract clearly states that when the park is closed, they need to close. If you think about it, it would be ridiculous to close the park, but then allow people in to camp there. A similar situation would an individual store owner within a mall - if the mall rules are we close at 10PM, then you need to close at 10PM. Sucks for the campground owners, but they signed the contract. Also, yes a small piece of the money earned by those concessions does go to the government, and we appreciate it - but those feed don’t come anywhere close to covering the costs of running a park.
Five, the major duties of the National Park Service are to protect, preserve, and interpret the resources of the National Parks. Those duties, as well as the boundaries of the parks themselves, are determined by Congress. When Congress decides to not fund the Park Service, the only option as the stewards of these national treasures is the lock the gates. I can assure you that if we didn’t lock down when there was no staff around, there would be people with metal detectors and shovels digging up battlefields, and trails being hacked across sensitive landscapes. Huge amounts of time are spent preventing people from doing stupid things - either trough malice or ignorance. And much of our budget goes to repairing damage to these sites.