He became Archer since all of them, Saber, Rin, Sakura, Ilya, Taiga and so on died and he could save nobody but himself (and the world =D). Soon after he couldnt even save himself, when he was betrayed by somebody he saved once and became a guardian spirit in order to protect humankind, even after his death.. he wasnt marrying anyone ._. sad gar story
I don't think Archer was ever married to Rin, actually. He certainly doesn't act like he was. He did have a wife, though, apparently, or at least a lover.
It's almost certainly Rin's grave, though, because the pendant he is holding is Rin's pendant, that she used in the war to save Shirou's life, and Archer always kept with him.
It's not actually known what happened to Rin or Sakura in Archer's world. It's quite likely that Sakura just got left behind when he went off fighting, since Archer never shows any real affection towards her (especially in HF), and he certainly doesn't seem to know of her treatment at Zouken's hands).
I think he made it up, actually. Or, rather, he made the bit about everyone dying up. The rest is canon, I thnk.
Archer's story is never actually told, in full. We only ever get to hear bits of it. The bit about being betrayed by someone he saved is canon, though, as is his reason for becoming a Counter Guardian.
The bits of his story that are known come from the game (Rin's dreams of him in UBW, and his statements), and from various supplimentary materials (that mostly aren't translated into English).