"Honey", "Babe" and "Sweetheart" I haven't heard yet. But I have heard "Dear" and "Darling", and it depends on how it's said and who's saying it.
Like the supermarket manager: I was standing in front of the fruit and veg display one morning and he happened to pass by and said, "XXX, darling, how are you?" Cracked me up. He knows me well, good guy. He's flirted with me once or twice in a joking and good way.
Once in a café a guy was leaving with his takeaway order, both hands full, couldn't open the door himself. So I opened it for him and he said, "Thank you, dear." A very friendly and sincere way of saying thanks. I quite liked it.
Here in Ireland what you'll hear quite often is "Good girl!", which usually will mean "Thanks!" or "Well done!" I've known women who don't like that. The "girl" part might sound a bit patronizing. But I don't mind it myself, given that I've always heard it in a friendly manner.