I'll start with the hero's shade. As has already been posted, this is a common one. I've come to this conclusion using a different set of evidence than most however. I don't see the Gilded Sword or Mirror Shield among his possessions, for one thing. His parting words after teaching the first hidden skill revealed much to me.
A look at the Japanese text specifies that the skills are "inherited only by blood relatives of the hero," and shows that "the one whose spirit is that of the sublime beast" refers to "the hero," not to "one who carries the blood..." This proves that both the hero's shade and Link are blood relatives of "the hero," given that their spirits are also of the sublime beast and they both (already/will) know the hidden skills.
The next quote reveals who "the hero" is.
The hero's shade is "the hero." Following Occam's Razor, we assume that there is only one "the hero" (besides the one that TP Link is to become) because there is no evidence or necessity for more. This hero is the Hero of Time, the only other hero to have wielded the Master Sword he seems to know so much about.
Now, all of that may seem pointless, as most people already accept this idea. But I'm going to delve deeper into these quotes (possibly too far) to learn more about what became of the Hero of Time. I'll look at the second quote first this time, specifically the second line. "I accepted life as a hero" - I'm almost certainly overanalyzing this - This sounds like a choice. The HoT didn't have much of a choice. He was told what to do. But Zelda felt bad about this and gave him to opportunity to make his own choices by sending him back in time. He must have chosen to be a hero sometime after this point. He couldn't have been referring to his journey in Termina because he didn't know the hidden skills at that point. It was during his "life as a hero" when he learned the lessons. So this life must have happened after he returned to Hyrule. This leads to the second bolded phrase of the section of my article I posted. He became the hero the people of TP remember sometime after both of the previous games. What exactly he did as a hero relates to the first bolded phrase. There was a war, though we don't have enough information to guess who it was with and what it was about.
How he died, however, still remains a mystery. My theory is that he forsaw the need for a new hero in the future in case Ganondorf escaped or a new evil would arise, and he found that the best way of aiding that hero was to create the howling stones and die in the Lost Woods to become a stalfos. Perhaps a battle was fought there as part of the war I mentioned earlier. This might have something to do with the ToT mystery as well, which I still haven't come across a sufficient explanation for.