As said, only thing that closes is the car park, which is run by the council. The rest of the forest (Crown Estate) is always open.
Laybys and side roads – be careful around The Lookout area. The layby right next to the start of the trails is a hot spot for giving people tickets. Though they tend to be there at busy periods. The road also has double yellows. Possibly why they ticket the layby though I’ve never been sure why they can do that as it’s off the road. Unless it’s blocking fire access or something like that.
Residential areas – keep it quiet at night.
Big area though and you can get in from any side.