I am getting ready to go tent camping (week of 6/15). I have a trailer which will allow me to take all my gatherings needed to spend a week. To what extent, if at all, are they allowed?

Yes

When I was there they were closed due to the virous. All the bathrooms and information centers were closed. I know they have campsites for both campers and tents. My family up that way has not went back there yet so I'm not sure if they have open back up. It's a beautiful place and the forest around the park burnt last year , but seems to be comming back to life.