Why I'm feeling hopeless about life? I'm so sorry. 
When I born as layman ; I tried to have loving life but it always come with big deal. She leave me undone and she wanted I must change my religion with her (muslim) to get married. I was ready but when she leave me , I just realise how silly I was. Now I'm completely distracted from life like I don't feel having family and I don't think a girl who know about my past will accept my love because she know I was ready for leaving Buddhism. She did asked me "Don't you think this is wrong ?". I want to apologize her and promising "I'll spent my whole life as Buddhism " . I don't know how to get rid off my state of mind ? I'm so sorry.
I guess the reason why you were feeling hopeless is that you were anxious about the past, a memory ... but the past isn't something you can conveniently change.

You were also anxious about the future ... "I don't think a girl who know about my past will accept my love" ... but the future too is something you can't easily change ... it's beyond your control at the moment (for example because it isn't happening yet) and because you can't control it it's easy to feel hopeless (or helpless) about it.

Instead of being "distracted from life" by anxiety about the past and future, maybe the one thing you can affect more easily, one thing you can reach, is the present. You're aware of what you're doing now, how you're thinking now ... maybe you can use Buddhist practices to relieve your suffering now, your present suffering ... maybe in fact that's something you can hope for, i.e. you can hope that Buddhism can help you.

Another reason why you might be feeling helpless is because "I tried to have loving life" -- a lot of people in society want that, but it maybe "hopeless" to depend on someone else loving you (again, because you can't control that).

FYI this answer has some advice on how to choose a marriage partner.

Also, is it true to say that "hope" isn't a big factor in Buddhism? There are things that are like hope, e.g. faith and confidence.

Hope is maybe similar to ignorance, e.g. you 'hope' that something is true when you don't 'know' that something is true. Maybe it's better to concentrate on what's knowable, on what makes sense, rather than trying to hope for what's unknown (and the future is maybe not just unknown but unknowable).

I found (only) a couple of essays by Thanissaro Bhikkhu about "hope". One is All About Change ... which says that it may be stressful to have "hope" in things that are impermanent. It then goes on to describe a search for "the Deathless" via concentration. You said "I born as layman" so, I don't know, maybe you're saying you're not interested in that ... but maybe the essay is worth reading anyway, because it's lucid and includes a question from the Buddha that's worth considering:


  "What, when I do it, will lead to my long-term well-being and happiness?"


Another short essay was a Dhamma talk about The Sublime Attitudes. It includes this quote:


  Notice that the teaching on equanimity is a reflection on the principle of karma. Of the four chants we have for the sublime attitudes, it's the only one that's simply a statement of fact. The others say:
  
  
    "May all beings be happy.
    May they be free from stress and pain.
    May they not be deprived of the good fortune they're experiencing."
  
  
  The first three are wishes, attitudes, things you would like to see happen. "May... May... May..." The fourth one is simply a reflection on the way things are.
  
  
    "All living beings are the owners of their actions, heir to their actions...
    Whatever they do, for good or for evil, to that will they fall heir."
  
  
  This reflection actually turns up in lots of different contexts. In the five reflections, the reflection on karma is the one that gives hope. You realize that you're in charge of your actions. You're not simply a victim of fate or of the stars or of some other being acting through you. You're the one who's making the choices. That's what gives you hope.


I guess the difference is that you can be hopeful about what you do (instead of trying to depend on someone else).