Yes, but typically only one type in store. They may have more online.
Yes. At least the one in Danvers MA has kitchen faucets. You could also check Costco.com
Yes, but I have only seen automated systems. Like many items in these big box stores, they are often carried as promotional items, not standard as in a hardware store or building center.
I've only seen faucets once, but I don't typically look for those types of materials at Costco😉
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