7 hour layover in Beijing

To be honest, time is rather tight.
Also, one hour is not enough to visit the Forbidden City. If you don't have the entry ticket booked in advance, it takes time to queue up to get one before entering. Let's say, you may need to spare half an hour to buy the ticket upon arrival and the left half an hour, it's just enough to tour around the first courtyard of the palace. So if possible, you'd better change your plan.

Thanks for your input Bruce

Now I calculated that it will take us almost 2,5 hour from that we land untill we get to Dongzhimen, is there a chance that we can make is in 1,5 hour if we are lucky with immigration and catch the train?
We are having our checked in luggage send to our final destination and entering on a 72-hour Visum Free

However we will take the train to Dongzhimen and it we make there before 11:30 we give it a try to have a look at the Forbidden City, otherwise we spend the hours around Dongzhimen.

How long is the cab ride between Forbidden City and Dongzhimen?

Yes, it's possible to make it 1.5 hours with immigration and catch the airport express if there won't too many arrival passengers.
It takes about 20-25 minutes by cab from Dongzhimen to Forbidden City. So if lucky, you can reach the site at around 12:00.
Your plan sounds nice. If time permits, go inside to visit the ancient palace. If not, tour around the Dongzhimen area and have a lunch there.