I don't know about purring. They can do a kind of cooing. I think most of their non-speech noises are throaty and vaguely bird-like.

They can learn human language, but their faces aren't made for human words so they're very into hand signs where spoken words fail. They have their own language (words/sounds/gestures), but it's not something they share with outsiders given the history with Empire Eutharious.