I don't think he died, the ending doesn't look sad to me..
About the other question, some say that after Link's awakening he got back to Hyrule only to discover that Ganon was back, and then Zelda 1 starts.
This theory is supported by the fact that in Link's awakening he was training for the return of Ganon, after defeating him in A Link to the past.
There is another theory, that says that Hyrule from a Link to the past is the new Hyrule from Spirit tracks, this would explain the timeline placement.
BTW there is no way LA can be is before WW