In the first days in a relationship, a girl welcomes a guy with "hey handsome". Would be "hey honey" an appropriate response?
The feminine equivalent to (usually, facetious) "Hey, handsome!" is...
There is a Hank Williams song in which he says the following:
"Hey, good looking, what you got cooking? How's about cooking something up with me?"
While these sentences may confuse you with their idiom concerning food, and in answer to your question, the way Hank Williams addresses his girlfriend is still used today: good looking, or good lookin'. It means simply you are looking good (i.e., attractive, pretty, lovely, pulchritudinous, beautiful, easy-to-look-at, easy on the eyes, appealing, and so on). In everyday speech you could also say, "Hey, beautiful!" but not "Hey, pulchritudinous" or "Hey, pretty (or lovely, or easy-to-look-at or appealing)" .
As for the cooking metaphor, Williams is saying simply "What's going on? What are you doing now? Let's do it together and create something pleasurable. "
In terms of words between a couple you are right that a girl can tell the boy "hey, handsome" and he can say "hey, honey."
If he was not her boyfriend, and he wanted to call a stranger girl "honey," then that wouldn't make sense because "honey" is an endearing (usually romantic) term for girls he knows.
If you wanted an equivalent word for "handsome" then "handsome" for girls can be used, but it is rare nowadays. You could use "pretty," "cute," or even "charming" when describing good-looking girls that you do or don't know personally; these terms are not romantic if you don't want them to be.