I think you may not be aware that AA has an All-Partner award and an AA OneWorld award, which are different.
The 125k award you mentioned is an All-Partner found here:
http://www.aa.com/apps/AAdvantage/Vi...artnersContent
You posted this message on the OneWorld board, and the AA OneWorld award is based on the distance travelled. In your case, this is a Zone 6 OneWorld award which costs 130k.
http://www.aa.com/content/aboutUs/on...horEvent=false
Main differences: The AllPartner lets you choose from more airlines, has limited stopover rules, and you can fly on as few as 1 airline if you choose. The OneWorld gives you multiple stopovers, but requires that you fly on at least 2 non-AA OneWorld partners.
You can read more about the latter award here:
http://www.flyertalk.com/forum/showthread.php?t=433366
Depending on what you want, your question may belong on the AA board instead.
To answer your first question, if you are able to get a OneWorld award to Hawaii and Fiji, then yes you are permitted to stopover in Hawaii.