How many hours I should spend on Mutianyu?
Unless you book a private car to the Mutianyu Great Wall, that takes 2.0-2.5hours(each way) form Beijing city to get there by public transportation. Mutianyu is actually the easiest of all to climb (0.5hour) - if you are not fit, you can take a cable car for a round trip. and 4 hours hiking is enough, even the all 22 turreted-fortresses.

What's the best way to traveling in Mutianyu?
Mutianyu is the favorite section to go, especially when you travel with kids. Try to take the cable car up to Fortress No 14, walk to No 6, and then take the lift chair or slide down from there. The kids like it a lot. It's always a pleasant experience.

Would it be feasible to cover both the Ming Tombs and Mutianyu in the same day?
Yes, Most people would to visit the two places in one day. Mutianyu is located in Huairou District and the Ming Tomb is located in Changping District, the Huairou is next to Changping in north part of Beijing, that about 1 hour driving. more info at Mutianyu + Ming Tomb Day Trip

What's the Best Season to Enjoy the Beautiful Leaves?
Oct.16 - 30, every year.

What is the cable car for and is it necessary to use?
The Mutianyu's cable car is used to help visitors ascend to the wall and go down from the wall. It depends on your plan and energy. If you have plenty time and energy, it is not necessary to use it. But if your time and energy are limited, you can choose the cable car to help you ascend the wall or go down from it. It is all up to you!

How much for a taxi to Mutianyu and back to Beijing city center?
A taxi would cost you about 800-900 RMB by the meter on(this is for a whole day). but haggling for that, they usually accept CNY 600-700 for this trip.

How to reach mutianyu by Bus?
Firstly, you should get to the Dongzhimen bus station(It close to Dongzhimen Subway Station), and take bus no.916 or no.936 to Huairou bus terminal station. and then you have to change a local bus or hire a taxi to Mutianyu Great Wall(17 km)!