It's open year round and I do not believe it is closed due to COVID but you should call 760-872-5000 to be certain. CG has a host sometimes but not always and does not have an on-site ranger booth.

I don't know. The website doesn't indicate a closure. Here's the website which has a phone number to call. https://www.blm.gov/visit/tuttle-creek-campground-0

The campground never closes. However, the water and dump station is closed when it gets colder.

I think you would best check the website. I don't personally know the answer.