If I get an email or I'm on skype with a Chinese, let's say, Johnny Ming, David Khan or Kathy Liu...

Believe me, they prefer to be called their title or Mr./Ms. + family name. And for business talk, it is not proper to put it down "take care, mate" (unless you are very familiar with each other).

Thanks, but it's hard to believe when it comes to European names. I mean, I had talked to many Chinese people via internet, when I was a supplier manager couple of years back and I was told by them, that's fine if they're using their English sounded names. And it was I, who was addressed by mate or dear at the end of the chats first, actually. A few times I was even told that it is a stereotype. So, still being confused, I'll wait for some Chinese "mate" to make it clear, cheers!

Yes, it is ok to call their English name, but "mate" is more used in our casual talks. Anyway, just as Iris mentioned, if you are familiar with each other, it is ok though for business talk.