Hutongs and should we do that main section of the Great Wall ?

Yes, no problem for you to see them by your own. I would recommend Nanluoguxiang, which is close to the north gate of Beihai Park, Shichahai, Bell Tower and Drum Tower, walkable from Yonghe Monastery and Guozijian. There are many hutongs around this area. You can just get around or take a rickshaw. Another one, Yandaixiejie, close to the Drum Tower is a good option too. As to the Great Wall, I don't think Mutianyu is easier to climb, but it is quieter and more beautiful, I think. They both have cable car and slide way facilities. Considering you knee problem, I would suggest you take cable up there and continue to walk a while as you can.