None of the above will entitle you to F lounge access in HKG as your departure flight is in business class.

At the connecting airports (SIN, NRT) you will be entitled to use the relevant F lounges as you are departing in F. In LAX if you can get access to the F lounge you are entitled to use it, same for the AA flagship lounge. Otherwise you can use the AAdmirals club.

OW lounge access rules for class of service are for the connecting point between oneworld flights, they don't determine the airport lounge at the point of origin. (Individual airlines may have more generous lounge access at the port of origin especially when travelling on mixed itineraries, but as you are mixing your airlines, CX will determine lounge access in HKG, and that's business class.)