L'Audauce, L'Audauce, tojours, L'Auduace.
Go for it. You only live once and you may end up regretting it one day that you never at least tried to find out the deal with this chick.
If I was a chick and I got your letter, I wouldnt think you were a stalker. It sounds like a pretty decent letter and you are telling her how you feel. Great love stories have to start somewhere and perhaps in 50 years, while you and her are celebrating your 50th wedding anniversary, both of you will have a nice story to tell your guests.
Dude, I say go for it!
Well, this would be a good story to tell, say, after you have been together for some time and you are already engaged. By which time she will know you well enough that she will be truly touched by the depth of your feelings, and won't have run shrieking into the night, which she will if you come at her with all of this. I could regale you with a precautionary tale from my own early naive dating experience, and it ended in disaster. You have some lady BBSers giving you the "don't" advice, which should carry much more weight than us males, and the males overwhelmingly have said "don't" as well. But I do encourage you to keep the letter, to read after more life experiences have made you wiser, both in your own self-knowledge as well as knowledgable in the ways of the fairer sex. And there are other ways to discover whether or not she is really involved in a relationship with another guy. You have a good heart and good intentions, but if you don't get the reaction you are desiring out of this (and I don't believe you will), you'll end up hurting yourself in the process.