"A duck is eating a cookie."
Translation:Kaczka je ciasteczko.
The 'rare for this word' comment referred to 'vocative plural'.
The Vocative case forms (singular and plural) exist for every noun (for plural ones they're identical to Nominative/Accusative plural), but they rarely make sense for words other than people and animals. Vocative is used when addressing someone. It's rather unlikely that you will talk to the cookies ;)
Example: the Vocative forms of "mama" and "tata" are "mamo" and "tato". So "Kocham cię, [mamo/tato]" is "I love you, [Mom/Dad]".
I'm not sure where you have seen those Polish translations before, but allow me to clarify.
"Herbatnik" is a kind of simple cookie, typically in a form of thin wafer. As the name suggests, it might be fitting for tea tasting.
"Ciasteczko" is your typical cookie with a flavor (chocolate for example). Though perhaps you may classify "herbatnik" as a kind of "ciasteczko".
At the moment I can't think of a situation where a cake would become "ciasteczko". If it's a really small cake, then it would probably be "ciastko". A celebratory kind of cake (like birthday or wedding cake) is "tort".
Depends on dialect, but in (?)British and Irish English a cookie would be a specific type of biscuit. A cookie is the type that has chocolate chips in it or something similar to that. A biscuit can be a cookie or can also be a digestive, rich tea, bourbon, Jammie Dodger, Crunch Cream, Oreo, Gingernut, etc. The above-mentioned "herbatnik" looks like it would also be a biscuit. Some people might even consider wafers and crackers to be biscuits. Does 'ciasteczko' incorporate different kinds such as digestives, etc?