I think we meant more like Fedex or UPS for mail. I wouldn't trust the USPS w/tickets either!

Yes--space available so choose wisely. Zeds are refundable. You should always ask about rollover to next flight. I have never had to interchange a zed--airline A to airline B. ID tkts are carrier specific--ID75, 90, etc. Parents usually pay higher zed level or ID % than employee.

I don't use gozed so I can't speak for it. Zed is for any flight city to city--any airline that has agreement w/AA.
I'm sure can tell you if AA works similar to DL--your daughter should be able do all of this w/relative ease on her company website.
I'd just get whatever you can to reach an AA gateway. I assume NRT, ICN are good options. I see Cathay via HKG as an option. Do you have a Low Cost Carrier in Philippines?
You could zed on DL to NRT.