Duck sauce is a name that was adapted in American Chinese cooking. The original product, which is used in Asia (particularly known with Canto food), is plum sauce. Same thing, though you may get a slightly different product depending on where it was made.
I live in a desert so extremely low humidity and the pantry area is often over 80. I’ve used potatoes over a month after buying them many times. I still use them for myself if they have small sprouts. I usually don’t see mold until closer to two months in. If I’m cooking for others I’ll buy fresh. Our local grocer has a very small selection of produce so I tend to buy a bunch of the nicer ones if I see they’ve restocked since the next grocery store is about an hour away. When I lived in the city though I’d only buy what I planned on using within the next couple days. More trips but always fresh.