Yes, it is appropriate to name an animal after a country. It does not matter what an animal is called in a particular language, as long as it is universally known and can be used in every day language. It is silly to read anything more into the naming of the bird we know in the U.S. as a turkey.
I don't know why it's called Turkey, but it is not necessarily derogatory. It means good things for most people and it could be considered an honor to name an animal after a country. It doesn't have to be a bad thing. It can be a really good thing for the country.
No, I don't think it's necessarily appropriate to intentionally name an animal after a country. But I think it happens. That's because words have different meanings in different places. If it's a coincidence that, for example, the word turkey sounds like a country, and the word peru sounds like a country, then we should just let it go.
No, it is not appropriate to name an animal after a country. Depending on the animal in question, naming an animal after a country may cause serious offense to the citizens of the country that the animal is named after. In an age of increasing animosity among nations, this would be a terrible thing.