It's only one segment if you transit TPE continuing on the same flight (i.e. one coupon = one segment). As such there's no point in taking the flight which stops in TPE, not least because by doing so you also avoid the excellent kaiseki meal which is only served in F on the HKG-NRT nonstops.

But you have two extra segments available so if you want to go to TPE just add in a HKG-TPE-HKG.

IST is still allowed with DXB.

As number6 says you either need to go BA transatlantic to Canada or use AA to the USA to get AA miles. Make sure you get a 777 Atlantic config if you take AA.

Remember that you can only have two stopovers within North America.