Dude, one Lingot for that avatar. You reminded me of my youth, and hours and hours spent playing DOOM 2 :)
This is the dative case. Kind words are pleasing for whom? - for a cat.
nominative - ко́шка
genitive - ко́шки
dative - ко́шке
accusative - ко́шку
instrumental - ко́шкой
prepositional - ко́шке
Ok. Now I understand in another sense. I thought «и» was only a conjunction, but as I see here, доброе слово и кошке приятно doesn't mean kind words and pleasing... What if I say only кошке приятно separately?
Доброе слово приятно кошке / Кошке приятно доброе слово = A kind word is pleasant to a cat. As you see, this does not make much of a saying. However, when you add "и" (which will have the meaning of "even"), this will imply that everyone (even a cat!) appreciates kind words.
If you say just "кошке приятно", that would mean "the cat is pleased".
Доброе слово и кошке приятно is correct. It means that even a cat understands kind, good words.
the pronunciaton for the singular "dobroe slovo" and for the plural "dobrye slova" seems the same, doesnt it?
No, they are different. You should hear the difference between "dob-rah-ye" and "dob-ry-ye", and the stress is different in "SLO-vah" (слово) and "slo-VAH" (слова).
I've discovered forvo.com, where you can enter words and hear them pronounced by real people. The audio here is not quite right - it's like "doh-bray" while the audios at forvo are more "Doh-brah-ye" which is what I would have gotten just sounding out the syllables. Check it out at: https://forvo.com/word/%D0%B4%D0%BE%D0%B1%D1%80%D0%BE%D0%B5/#ru