Why does Yuno fall for Yuki in the first place? It occurred to me that in the whole anime, there is never any reason mentioned for why she falls in love with Yuki. I mean, the first Yuno from the first dimension loved him as much as the Yuno from the second dimension and so on the third (probably). But there was never any explanation for why that made her like him so much. Is there anything that explain that in the manga? or somewhere else?
Darjeeling's answer is right about the things that made Yuno falls for Yuki, but as far as I remember, there's deeper truth behind that:

 Yuki wanted to go stargazing with his family, but his parent got divorced. So Yuno answered that she will be his bride, his family, so that Yuki's wish might come true. And to Yuno's answer, Yuki replied that they had to become adult first. The important thing was, later it was told that, at that time, Yuno's parents HAD already dies. She might seem OK, but she had actually fallen deep into despair, thinking that there's no future for her. And that was where the stargazing conversation happened, in which Yuki (kinda) promised to take her as his bride. Thus, that event gave her a new hope, a future as Yuki's wife.

So, without Yuki himself realizing, at that time, he saved Yuno with his words, and that event became a life support for Yuno.
I forgot the chapter of manga where that complete reason is revealed, but for sure it's not an early chapters, since a big, big secret

 The story about how Yuno's parents death

has to be revealed first. Though I remember that when it was revealed, Yuki himself realized that

 &quot;So I've became her only moral support...&quot; or something along that line