Have I made a translation mistake?

Even a small comment would be appreciated, thanks.

I was recently chatting with my Russian friend using translation software. She had just shown me a picture of her with a hamster. I have a small dog not much bigger than it. I was trying to make fun of my dog (Kigen) being so small. I then attempted to tell her that my dog was crying to go outside and steal food from my cat. I think my words may have been interpretted as though I called the hamster cat food? What do you think, and also your opinions on her final chat line as well as my follow-up SMS. Thank you very much for your help on this.
Chat:
Eric Oathes says: Просто красивый! Simply beautiful! Thank you
Eric Oathes says: Маленькое животное почти размер Kigen!
Екатерина says: очень смешно
Екатерина says: не издевайся
Eric Oathes says: Moya Kigen, on юмор
Eric Oathes says: Он маленький как хомяк !!
Екатерина says: да уж
Eric Oathes says: Он кричащий в двери теперь
Екатерина says: :D
Eric Oathes says: он желает пойти, едят пищу кота
Eric Oathes says: пища koshka
Екатерина says: нахал у него своей нет?

Follow-up SMS:
Ya proshoo,chto Vi nye doomayetye,chto ya nazivayoo homyaka(pishsha kota).Moya sobaka probovala ookrast(pishsha kota), poskol'koo mi govorili.Ya loobloo homyaka

Thanks again for your time :)