Almost always within 48 hours, unless a weekend gets in the way.
If you don't have TRIPS access and associated authorised credit card use, they will ask you to visit your local EK town office to pay for any tickets. A re-listing would probably also require an email....but I have known sympathetic airport staff help out in cases of last minute denied boarding at the airport. Your onload priority would depend on your grade while you were employed by EK and would be shown on your ticket. As a retired Boeing Capt with 20 years service, my onload priority is '33' using my SRC tickets, so no, you're not exactly top of the list.
I'm a little puzzled how you'd have SRC tickets if you're not employed by or retired from EK, and also don't have TRIPS access? Probably none of my business anyway........
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7B