Re: my fiance is cheating on me??
As people have said the password isn't the issue here, but I will say he didn't actually decline to give it because he felt it was an invasion of his privacy (as many people are suggesting), but instead made other excuses. If I were in your shoes fact that he declined for reasons other than privacy would raise my suspicions too.
I am astounded that your mother has tried to turn it back on you? Is she really that desperate to get you married? I realise izzat etc is at stake, but a broken engaement is far better than a broken marriage and/or a life of misery. No mother would want that.
I would speak to your mum again. Print off emails (if they're still there), otherwise explain clearly verbatim what the content of the emails he sent was. It is NOT right or appropriate for him to maintain ANY level of intimacy with females. Female friends/work colleagues - fine, but if his interaction with them is anyway romantic then that is in no way acceptable.
You do also need to speak to him again, burying your head in the sand won't make the situation better or go away. Yes it's hard knowing what to say, however this is the guy your planning to spend the rest of your life with, you should be able to approach him with any of your concerns, and he should be man enough to listen to them and respond accordingly.
I'd start by explaining clearly to him why you wanted his password, that you weren't expecting to find anything, but when you looked at the sent items you found some emails that unfortunatley are causing you so worry, and making you wonder about his commitment to you and the marriage. Ask him to explain to you what those emails were about - give him a chance to defend himself, but say to him that you're not stupid and not to patronise you in assuming you'll believe him in saying it was his friend that sent it. If he does say that, ask why is it ok for his friend to have access to his account, but not you?
Say to him you want the truth, and that you are prepared to take it no matter how much it hurts - if he's had any kind of (virtual) relationship, then to be open and honest with you. As only then can you both decide what to do in the future, and how to build a strong and healthy relationship. IF that's what you want.
Do not allow him to stray and come back at you with the 'if you hadn't been snooping argument' - just say to him, what's done is done, but we now need to tackle the issue hand.
Once you've had this discussion, go back to your parents and tell them what was said, so that they can help you make the right decision, if you don't feel well equipped.