Yes, all these names for cat are from a common origin including the French chat, German katze, greek γάτα and many more. I think only the Asian languages, Polynesian, Native American languages, Indian and Klingon that I know of don't have the same root for cat. Others probably know of other languages as well. But basically most semitic and indoEuropean languages have a common root for it.
(1) "is it usually the VSO order?"
Yes it is. However, the sentence above is not a verbal sentence جملة فعلية -- but a nominal sentence جملة اسمية, ie. subject + predictive adj./complement مبتدأ + خبر so there is no verb.
(2) "is عند conjugated"
I don't understand what "conjugated" means here. 3inda is not a verb, but something like a preposition in English. "3inda 2arwaa" is "jarr majrur" جر مجرور which 2arwaa is majrur. We put "qiTT(un)" قطة because it is mubtada2 nakira مبتدأ نكرة without any "musawwigh" مسوغ so qiTT(un) should be with the "khabar muqaddam" خبر مقدم (the complement) -- I am so sorry for my limited English, that's how we learn Arabic in my country. We don't translate the Arabic terms into our language. When I have to translate them into English, my comments become awful, hmm I should edit many things now?
Nb: I am wondering why some native Arabic speakers never explain us by using Arabic terms but only English terms, which we know that both are not the same!