Bought tickets in and out of Shanghai with other airlines to Hong Kong and Bali

My wife and I bought tickets to Shanghai from LAX. We were planning to buy a 1 way ticket 2 days after arriving in PVG to Hong Kong (stay for 3 days), from there buy another ticket to Bali (stay for 5 days), and then buy another ticket to PVG for less than a day before our returned ticket back to LAX.

We are both Americans. Can we use this visa-free transit? Do we need to line anything up before with our airlines?