It's so very sad to hear of a tragedy like this, and hard not to think of the emotional pain he was in and the shock, pain and grief he left behind. And regardless of how close you were to this friend, I'm sensing that your deep empathy for others is a part of who you are as a person.
It's a rare and wonderful gift, even though in times like this it may not feel like it. Yes, as wildcat says, when you're emotionally fragile it can cross over into hypersensitivity, but otherwise it's what makes you the warm, kind, compassionate person that you are.
I also read in your words a sense of helplessness because you want to help but you're so far away -- the letter is a great idea, and remember that your friend has others around her and isn't alone in this. (My brother's cat died when I was living on the other side of the world -- I cried for 2 days and I wasn't even depressed at the time. At the time, I felt ridiculous for crying like that over a cat, but later realized that it wan't the cat I was crying for -- more a sense that my home, my stability, had changed while I was away... or something like that)
As the others said, allow yourself to feel, to grieve, because it's a sad, sad thing that has happened. And cherish your caring nature.