"Hi, Aussie.
Welcome aboard!

I actually doubt if "Aussie" sounds ok in this context. I cannot feel that. I hope it doesn't sound offensive."

Perfectly fine, there's no reason the term "Aussie" should ever be offensive to Australians, thanks for your welcome

"I don't think that Eremenko is a rather common surname in Russia.
At least it's not among the top 100 most common surnames as I just looked up, yet it's not unique.
It's of Ukrainian origin because of its suffix -enko."

That's very interesting, thank you for that information, it will help me very much in my search for the family records Hopefully some day I'll have the chance to visit both Ukraine and Russia, might find some more leads about the family.