It's not something that is commonly said, no. Of course, it is perfectly understandable, and I suppose that a man might say it to a woman he likes, but it would be helpful to know the exact situation you are talking about. What is the relationship between the man and woman, how are they communicating, and what is the man trying to convey? (That is, is he trying to be romantic or just neutral?)
Just to make things more clear. The person who wrote that is a Japanese man. He wrote it to me and I am not Japanese.
It's a new friendship between a man and a woman. So I'd same our "social status" is the same. Both adults and not work-related.
We haven't met in person yet. That's why it is harder to understand what he's trying to convey.
I know nothing about Japanese men and I am still getting mixed feelings about this. I am not sure how they interact with women. Also, I am not so fluent in Japanese to be able to understand all the nuances. We definitely use informal language to communicate. I guess I will just have to wait and see. The only thing is I don't want to sound too forward because I misunderstand him, so I will keep it as neutral as possible. Thank you!
Okay. So kokoro 16 is a woman and a native English speaker, right?
Your explanation of the context and background in #3 made things clear.
The guy just wanted to write "Good night. Have a nice dream ❣ " in Japanese.
良い夢を❣ is not a common traditional Japanese expression, so I strongly felt it as the "directly-translated style Japanese."
And I didn't know why the writer intentionally chose that style, which seems a little bit funny to my ears in a certain viewpoint.
But now it's clear that he wanted to write "the typical parting greetings of English" in Japanese.
As Japanese, or as a non-native English speaker, I think "Good night. Have a nice dream!" is the typical greetings in English, no matter if it's not true to native speakers.
He didn't think he could convey something more than the parting greetings, I bet.
The last ❣ may convey his positive feeling to you, but it doesn't necessarily mean that he wanted to become intimate with you.
But I don't know what he is thinking about about you because I'm not him.
Apparently, he wanted to be a good friend with you. But we cannot guess he wanted more than a good friend or not.