AA flies from PHX only to ORD and DFW and sometimes MIA (seasonal?). A single flight number PHX-ORD-IAH is not plausible, but PHX-DFW-IAH could be a through flight. I just checked aa.com and it doesn't operate for the date I tried, however AA changes the through flights every quarter. If you do see it, book it right away with a fixed date; as long as you can travel on that date, AA will reroute you (onto 2 flights) and it will count as 1 flight for the OWE rules (whereas without such protection you would have to pay a change fee of USD 125 and find a routing with 1 sector or change other routings in your ticket).

Historically there have been fare increases in OWE during the first quarter of each year, often in Jan. When Oneworld thinks a currency change is permament and not just a blip then it raises the fare (often to higher than the ex-US fare, to allow for future currency fluctuation), or switches to USD. If the ex-ICN fare is important to you, booking it now (before Dec. 31) is the only safe strategy.

As for redeeming an F ticket on CX LHR-HKG, the chances are zero in my estimation. CX is reducing F capacity out of LHR and award availability has been running at close to zero for a long time. BA should be much easier to get, also you can route via NRT on JL or BA. Of course "impossible" awards do exist -- a few people get them each year, it just depends on your luck and persistence. But remember that Asiamiles members can waitlist for an award, whereas the rest of Oneworld cannot -- so seats go to the waitlist, as they become available. And even Asiamiles Diamonds (a "higher" tier than BA Gold, in practice) cannot get F awards LHR-HKG these days.