Now with your responses, it clearly was no-brainer, really -- I have booked non-stops, TG657 (777-200/200ER) inbound and TG658 (777-300) outbound.
I'll surely ask an attendant for mother's memento, thanks for mentioning it, BKKROP!
As for the birds, the schedule says either 777-200/777-200ER or 777-300 for all of the flights I looked at -- no sign of Airbus to or from ICN, but surely it's subject to last-minute substitutions. Which I hear is unfortunately quite common.
Thanks you all for your kind inputs!