PP The point is that OP wants to know whether the seat is available before deciding whether to commit to the booking or to try an alternative flight. Cathay's website allows you to choose the seats before you pay (or at least it did when I last used it) but SQ's does not, I think. And if you switch your flight after paying, there is often a penalty. I also empathise with OP about the SQ call centre: there is nothing worse than listening to a recorded message for 30 minutes that tells you to use their website instead - when you know full that the website does not provide the service you want (such as buying a separate seat for a child under two years old).
I just used to add a year to his age when I did the online booking. No-one ever queried it at check-in.
Agree about call centre. I was on hold fo 20 minutes at 5am last week when I called to cancel Scummy Daddy's flight that morning due to illness. Then got some blithering idiot who kept forgetting to put her mouth near the phone.