The updates on his fb are trying to install a fear of loss into. Like that like you said, he is having a great time without you. Maybe thats not the case at all. His hamster died.. hmm maybe if it was a dog or something that you both did together but hamster??? The cage bit was just a ploy to either him try and come around or you come to his. Why cant he just say, look is it ok that we hang out etc. honesty is the best policy sometimes i feel. And i have always been honest in all my relationships.. Maybe thats the reason im in this mess.
Look at it from this point of view,, if he had as his staus on fb that he was missing you and wanted you back and kept putting things on about you, im sure you would just think that as being soppy. Although its hard to tell from person to person, but on the whole, people feel sorry for you. Sounds like he is trying to make you believe he is moving on with his life, when really he might be waiting for you to make a move so he can assess if he has that chance again..
i really cant tell you if its a good idea to write the letter or not. As im also at this point in that i want the second chance and i hope i get it. But just not yet it seems for now..
If you love him and think the second chance is the way to go, it cant hurt by writing the letter and telling him how you feel.. its then up to him weather he wants to go down that road. But you have to tell him in the letter that there is a cut off period. He surely cant expect you to be there for years/months later after the letter has been sent to try and pick it up again..
I really wish you good luck if you go ahead and send the letter. I only hope i get the chance he is getting with you if you do.