Usually "for" me would be the more common term used but yes they are both quite correct :)

They are both correct. 'From' in this case, is more specified than 'for'.

I agree with Greg. “For” is what I would hear here. Also to be considered, “give him my greetings”.

Both are correct. In South Africa I hear both. Say hi to Stephen for me - this is like asking someone to do a favour for me. Say hi to Stephen from me - is more like send greetings from me.

As an American English speaker, I would never say "from me", when using the verb "say" or "tell". I use "from" when I am asking someone to give something from me on my behalf. Perhaps there are geographical / cultural differences here(?)