144 Hour visa question. US citizen going to Japan and China.

Hi. I am from the US and I am planning to visit China and Japan sometime within the next few years. I am planning on flying to Japan and staying for a few days and then flying to Beijing and staying in Beijing for about four days. If I have a layover in Hong Kong or South Korea on my flight from Japan to Beijing, will I need to apply for a China tourist visa? If I had a layover in Hong Kong or South Korea, I would not be leaving the airport, it would just be a layover.

The route would look like this:
Japan -> South Korea or Hong Kong (layover without leaving the airport) -> Beijing

I also plan to visit the Great Wall on my trip to China. Is the Great Wall technically part of Beijing and would I need a visa if I was going to see it?