You can fly from TLV via LHR to MEL/SYD.
I told you in the beginning of the post to trust me, why do you keep on going in circles and don't just pick up the phone.
About elal, I believe they are what I call a semi partner, so you can use AA to book elal, however it won't be a standard by them.
But, say AA 6006, operated by etihad going from AUH-JFK cannot be booked with AA miles, as they are only codeshare (even less then semi partner).
Aa with elal, is about the same connection as CO with Virgin.