I don't think in the mails the sender ever mentioned his genre. He kept talking with "I" and "you" that don't actually get you an idea about the genre. Also, nobody told her that the late owner was a guy, they just said the owner is sick and isn't coming back for a while. She saw the painting so she assumed by herself that it was a painting of the owner, when in reality it wasn't. that's why she got confused and thought the owner was a girl and that's why the story was told from a girl's perspective when in the end was the boy's perspective. In the korean drama this thing's better explained. I suggest you watch that one too, it has the same name as the manhwa :) .
Also, the painting was of her, but it was made through the viewer's heart. just like she said: "I'm not that pretty." So the painting didn't look anything like her, it was her portrait through his eyes, so still, it was her.

She finds her Daddy long legs just too lose him soon after

... that the emails are sent from a woman's perspective. The 'flashbacks' also show things from the perspective of the girl in the painting, which I guess is Young-Mi's imagination, but it's very confusing. This is the only real mystery to me... I still don't get it. Why were the emails written that way? It was just a plot device. I never figured out who the girl in that painting is. I would have said it is supposed to be Young-Mi but it doesn't look like her and no one seems to think it's her.

Edit/update: Korean (like many other languages) is a somewhat gendered language to the point that you can often tell the gender of someone by looking at how they talk (without seeing or hearing them). I still think the gender confusion is a weakness on the part of the author because she couldn't find a good way to keep the author's identity a secret. It makes more sense to say that the boy wanted it kept a secret so he wrote it from a different gender, but I'm still not seeing it.

It's really sad when Joon Ho don't remember he is Daddy Long Leg!