I remember thinking that same thing during this drama.

It's supposed to be weird. It gives it a forbidden love affect, despite that the two girls aren't related. (Or I think they're not related, haven't completed the drama yet! But I doubt they'd take that kind of twist.)

Ah, but the main story wouldn't have worked if they weren't identical. Actually the whole story would have fallen apart, unless they had taken it a completely different way. Especially to get the substitute bride.

I think it would have been sweet if instead of falling for a girl who looks like his sister, he would have found another sister in her. Brotherly love! It could have been really sweet. And created plenty of drama. He wants to protect and help both of his sisters!

i think i saw somewhere (cant remember which episode) hongki said that they are half-siblings

Yeah, it feels weird at first but when you think about it, he doesn't see Doo Rim as an identical of his sister and actually sees her as a whole different person so I guess you can say he ignored her facial attributes and fell in love with her personality.

I think he loved her like a sister, but since he knew she wasn't he felt like he had to try for more. Or maybe that's because I felt like the script was pushing it too much? It was a rather strange situation... Also I agree with Queen_Makjang, I think the point was to show how endearing Doo Rim was. 

But Yi Hyun is not blood related to them. He is not related to Na Doo Rim and he is not blood related Jang Yi Kyung.
He is falling for the girl that looks like his step-sister only because he had feeling for his step-sister.  But once again he is not his real brother at all, and this is made very clear at the beginning of the story that these two siblings are not blood related at all. Maybe I happened to watch a version with better subtitles :)