Okay one way of twisting the scene around: ......She ran out into the storm. The neighbour came to investigate and found her unconscious (coz of the shock or may be she bumped into something). He took her to the hospital and waited till she woke up. She was awake calmer and when she inquired the nurses told her where she was and who brought her in. The neighbour came in and introduced himself. You can built on this. I think this will solve your trust issues and also the neighbour won't be seen as taking advantage.
This as in what? The opening scene is just that: a showing of how things are at present, before any sort of assistance, to show all those problems that have been festering and manifesting, as well as a point to introduce the characters in an exceedingly dramatic fashion. It just would be out of place if done later because the issues are being addressed, rather than bottled up.
I'm also using it as an explanation that the situation I want, the thing I'm trying to accomplish is inconsistent with the behavior of the characters.
If a character has been raped at 14 (I'm assuming that is what you mean), it is highly unlikely that a 30-something year old man try to 'heal' her by having sex with her, for any other reason than selfish motives. It certainly would not help this character. I think you need to do a lot more research into the issues you are trying to write about. If you don't, you just have an incredibly unrealistic and quite shallow story. If a character has experienced this type of abuse, perhaps a friend or neighbour can be instrumental in the healing process, but it would not be by the means you have mentioned. If you need your neighbour to be 30-something, then why not just make the character who has been abused a lot older. It is quite plausible that a character would bottle up something like this for a long time. If they are of a similar age it makes it a lot easier to describe a sexual relationship without it seeming like the neighbour is also an abuser. If you want your neighbour to be a morally decent character (of course it is quite possible for the story to work if he isn't) then why not just make them friends? They can still meet in the way you describe, but perhaps experience a relationship based more on mutual healing (this means he would need something in his past he too has to come to terms with) instead of the man 'healing' the young woman. What are you actually trying to accomplish with the story?