Don't you know the difference between Czech and Polish?..
I know the difference, I didn't notice that that was referring to Czech, not to Polish :)
Vlad, could "kotyczka" be Russian as well, or only Polish?
Did you mean "kociczka" (a diminutive from "kocica")? There is nothing like "kotyczka" in Polish. I have even checked in Google and it finds only people with such a surname - but no uses of this word as a normal common noun in Polish.
About Turkish word origins - in Russian tea is "czaj", the same as in Turkish. And I know that in many European languages the name of this drink is either similar to English "tea", German "Tee" etc. or to the Turkish/Russian "chay". Polish is here unusual with its own word "herbata" :)
The Polish word for a carpet - "dywan" - also, I think (as far as I remember), comes from Turkish. But doesn't the same word in Russian mean something different? From primary school Russian lessons I remember a poem for children about a lady who was travelling and took many strange things as a luggage (the title was "Sdawała dama bagaż"), and she had also a "diwan" with her. As far as I remind it myself, it wasn't a carpet, but something different (although, of course, also irrational).
I have checked, and "diwan" in Russian means... a sofa :) In Polish, as I have already written, "dywan" means a carpet. But a sofa is even more irrational to take as a luggage than a carpet, so knowing the Russian words you have yet more fun reading this poem :)
I was once on a camp, where the meals were prepared by a cook who was from Slovakia or Czech Republic (I don't remember this exactly). And he called a glass pot with tea "czajnik". In Polish "czajnik" is a kettle. Such a pot, like the one that this cook was calling "czajnik", is in Polish "dzbanek" :)
Sometimes when Polish children are learning writing, and they have problems with ortography of the words where for example rz doesn't change in r in any of its forms (it's called an "exception"), parents or teachers are explaining that for example rzeka is in Russian "rjeka" (which is, BTW, AFAIK, an improper pronounciation, it should be pronounced "rika", at least they learned me it so later on, on Russian lessons - is it true, Vlad?) so that when the child remembers the Russian translation, it's easier to remember that the Polish word should be written "rzeka" and not "żeka". Another example might be "morze", which, AFAIK, is supposed to be in Russian "morje".