-As long as you buy ticket, you can visit Forbidden city. :)
-If you want to leave, you can, No body care this.
-Lots of Chinese can speak English.
-You can use cell phones, but no photo.
-You should leave Forbidden city when it close.
-kids isuuse is a hard problem, i cant help you.
-one week is so so.

well, with all due respect, I think you are kidding about throwing out all these questions. Since you know how to surf on internet, go google the Forbidden City first and then ask a decent question as a tourist. No offense.

well, in case you really don't know the answers to your question after googling the forbidden city, here are the answers you are looking for:
Forbidden city is a tourist cite, it was the palace where the emperors lived and worked, but now it's a museum. You don't need a permit to visit but you do need to buy tickets. It opens everyday from the around 8am to 16pm (go check the exact time by yourself when you are there). So you have to leave before it closes. There are no residents in the forbidden city, but they do have staff working there. They can speak a little English, I guess. You don't need to communicate with anyone, except when you are about to entering into places not opened. I don't think it's appropriate to leave your children to the staff there, because they all have work to do. There is no kingdergarden or kid;s playground there, so I'm afraind it's not a good idea not to take them with you all the time.
You can visit the City again and agian within a week everyday if you want to.