The booking office is Gamewatchers Safaris in Nairobi. Take another look at the website and there is a tab headed "Contact Us" which gives the contact details.

Yes it is certainly possible to stay 1 night and Nairobi Tented Camp also offers a pick-up service from the airport as well as arranging visits to the the nearby Elephant Orphanage. Jake Grieves-Cook, Gamewatchers Safaris

It is located inside the Nairobi National Park.

It is possible to get to the camp in a vehicle without 4WD like a minibus or a vehicle with high clearance but 4x4 is recommended especially when there has been rain and it is muddy. However you can also arrange when booking with Nairobi Tented Camp that their camp 4x4 will meet you at the Nairobi National Park gate and you can park you car and leave it there.

On the game drives, yes. Children of any age can go. At the tented camp, there is a small common area that includes a tent set up as a lounge, the dining tent, and a small area outside of it. Our ten year old found a stick and was able to entertain himself, but for other kids it might not be enough if they are used to being able to explore. Because it is in the reserve, any kind of animal could traipse through at any time, so the outdoor open area is limited.