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...
Pretty or beautiful are the most common words.
Handsome can be used for women, but is somewhat old-fashioned.
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. "