Part 1 -
The author of Mark (generally agreed to be the first written of the three synoptic gospels) makes use of the Greek ‘mythic hero archetype template’ in his telling of the Jesus story. This is a ‘template’ a Greek audience would have been very familiar with (it’s essentially the same template as Homer’s Iliad).
In this template, once the ‘father’ figure’s role in the story has been competed, typically coinciding to when the ‘hero’ (in this case, Jesus) comes of age, he is simply dropped from the narrative never to be seen or heard from again. This is a common literary device, done so that the main focus can now be placed on the ‘hero’ of the story. It does not mean the ‘father’ figure is dead, just that his ‘job’/’role’ in the story is done so he’s simply written out of the remaining narrative.
This concept of writing the parental figures out of a narrative so focus can be placed on the ‘hero/heroine’ of the story (the son/daughter) has European parallels as well; particularly in ‘hero/heroine’ folk tales. It’s more or less formulaic: in order for the hero to come into his own, the leading male figure (typically the father) usually meets some untimely demise (at least in the European formula). Same for the heroine’s mother.
We have, of course, a missing period of time of about 20 years in the Jesus story (from roughly the ages of 13-30-ish). He’s about 13 when his story suddenly stops. In many models, it is during this time where the hero/heroine faces many challenges and adventures that shape his/her character as an adult. In the Jesus story, this period is just a void and we are left to our own devices as to what took place. When we see Jesus next, he is an adult embarking upon his mission. Jesus seems to now take on the role of ‘head of household’ with respect to Mary. The ‘hero’ of the epic has emerged as the main focal point. It’s interesting to note (and perhaps further evidences the author’s use of this template) that Mary and Jesus never once refer to Joseph after Jesus attains adulthood. He just completely drops off the face of the earth.
The point is, is that even though Joseph is never referred to again (except in a few indirect references, e.g. where Jesus is called the “son of the carpenter”, the “son of Joseph”), it does not equate to his being deceased.