Are there showers & bathrooms?

Showers and flushing toilets available in the campgrounds. Some trailheads have flushing toilets. Group campground has latrines. Portapotties elsewhere. Visitor center opens in Dec 2018.

There are restrooms at most of the attractions; however, most of them are port-a-potties, no public use showers other than what the camp or cabins offer.

We stayed at Greenbrier Cabin. It had a shower, a bathroom, a hot tub and AC in every room.

In the campground area yes

Depends on where you're staying. Each camp site will have its own amenities.