It is all on CX metal or CX flight numbers? If they are CX flight numbers, then yes, you earn 0 AA miles. If they are AA flight numbers even they are CX metal, you will earn AA miles.

Again, the fare code comes into play when it is CX flight number, then only Y, B and H would earn AA miles.

However, CX allows lower fare codes to earn Asiamiles, albeit not 100%.

I am not sure L fare would earn Asiamiles. You should check CX rules. May be it would earn 50% may be it earns 0. If it earns 50%, it pays to sign up Asiamiles account though you need to know Asiamiles expire in 3 years from time earned and there is no way to extend it. You also need to study CX award chart to determine if your future flights would allow you earn ENOUGH CX miles for any meaningful redemption.

Take time to read the respective program rules - far better time spent than posting here - for I have seen in the 2 threads you started, there were less than 5 posts out of 6 pages so far, have actually addressed the issue of eligibility to earn miles based on your fare paid. But this is the premise of everything that follows! Without first figure that thing out, everything else is moot.