Could someone please tell me how to get from Beijing Airport to Forbidden City and then to Tianamen Square and back to the airport?

From the airport, you can take the airport shuttle bus line 2 to reach its terminal at Xidan. Then you can easily take a walk to reach Forbidden City. The shuttle bus to Xidan takes about one hour to an hour and a half.

If the nine hours does not include the time in the airport, it is enough to cover the Forbidden City and the Tiananmen Square in general, otherwise, the time is not enough.