and yes to your 2nd/3rd questions.

if taking AA from rio-N.A.-europe, u can stay at USA not more than 24 hours, same for your trip from europe-OZ passing via Asia (bkk/sin).
ba has better product trnastlantic than aa, i wd suggest taking ba unless u r AADV member. but it makes sense to go via NA if u want more miles
from what i hear on this board, avoid IB at if u can (LA is decent)