Is Link Dead in Majora's Mask?

[S.Peelman]

I haven't watched the video, but I'm fairly certain Link in Majora's Mask is not dead.

For starters we know the intro of the game takes place in Hyrule. Or at least, in the same plain of existence as Hyrule. Link is robbed by the very real, very alive and very same Skull Kid from Ocarina of Time. The Skull Kid (or rather, the Mask) obviously knows what it's doing, because it goes immediately for the 'portal' to Termina. It has been confirmed that Termina is in a parallel dimension to Hyrule.
Also, if Link were dead, how could he meet with the Happy Mask Salesman? The Mask Salesman is obviously the same as the one in Ocarina of Time, and he even implies certain events about Majora's Mask's predecessor. At the end of the game, Link is seen riding through the very same forest as in the beginning of the game, meaning he made it out of Termina again.
Lastly, the ghost warrior in Twilight Princess, called the Hero's Shade, is confirmed to be the spirit of Ocarina/Majora's Link. Twilight Princess is on Majora's timeline, yet he seems to have been an adult. There's also more things in Twilight Princess that hint towards the Hero of Time, yet couldn't have been his if he didn't live out to be an adult like the 'Hero's Bow'.