What access do chinese citizens and tourists have to the Forbidden City?

Yes, some parts of the palace is off-limits to visitors (both citizens and tourists). They have turned most part of the palace into a museum for visitors. I don't remember which parts are off-limits, since it's been over 10 years since I've been there, but I do remember you follow a "tour path" inside the palace.

It is open to tourists, and some areas are closed, but you can spend hours walking around.

It is now a tourist attraction and all can visit.