Hope someone can help me on this issue.

Can I book a codeshare flight with airline X, if the leg is totally external to its country and it's operated by airline Y?

For instance:

FCO-HKG, QF3860/CX0292, CX metal, looks like available if booked as first leg of FCO-HKG-SYD on QF, but it doesn't appear anymore as a QF flight available itself, nor at qantas.com, nor at oneworld.com although it was available some weeks ago on a third party website

(FCO-)LHR-HKG, BA 0551 + QF 0030 (QF 0030 on QF metal), looks available everywhere

FCO - MAD LA 5709 (Iberia metal) availabe for booking at lan.com and scheduled at oneworld.com only as a first leg of any flight to Lan countries, whether on Lan metal or not (eg LA 5709 + LA 705, FCO - SCL), but not as a flight FCO - MAD

Can I ask staff to book the codeshare flights under my preferred code, or can I change code after booking?

I'd like to do it on line to get promos or lower fees.

That would be very helpful for me in order to get EQS and attain status.

Thank you