Is the camp ground open for walking

Well it's not really a campground as it's main purpose. It's a state park with a campground. It's open year round as a park, so yes, you can walk, hike, bike there

2 week max stay limit

The whole past is open to visitors (bike, hike, run) year round, camping is seasonal but ground remain open for other activities

The campground itself is closed for the season

The entire park is suitable for walking. There are many asphalt paths and quite a lot of "real" off-pavement dirt trails. It is also quite popular with off-road/mountain bikers.

I believe so. Either way there's plenty of places to park.