O fare basis code is a deeply discounted ticket and naturally comes with more restrictions than others. I don't recall if the 3-week stay rule is particular to O fare. You need to read the fare rules or ask your travel agent for the specifics of each fare. In my experience, though, I have never seen an O fare as an AA codeshare flight operated by CX.

For CX flights (with CX number), you need H fare or above to earn miles on AA. Hope this helps.