1.) Why is he so hidden? We know next to nothing about him, not even when he died.
I don’t think he’s that hidden, given that Mary only appears a very few times in the Gospels as well. There is a school of thought that he was very humble and that he did not put himself front and center but always put Mary and Jesus before himself, which would be one reason we don’t hear a lot about him. Another reason would be that because he died well before Jesus’ public life, those compiling the material for the early gospels didn’t know him so they couldn’t include tons of material about him.
However, he has certainly responded to those over the centuries who were devoted to him, such as St. Andre Bessette. There are also private revelations, some of them approved to some level, where the visionary saw Joseph, or learned about Joseph and promoted devotion to him, or stated that Joseph’s tomb would eventually be found and the world would appreciate the importance of Joseph. Some Popes have already begun to appreciate him, such as Pope Benedict XV who entrusted the faithful to his care during WWI in
Bonum sane, and added him to the Divine Praises. If you want to know St. Joseph, just pray to him.
2.) If Jesus chose to come into the world through Immaculate Conception, why did he have a human "father " at all, especially one He makes no mention of?
For the same reason any boy needs a human father. To protect him and his mother, teach him, be a good role model. Jesus was fully human. He needed a dad on earth, especially in a society where single moms had no way of earning money, had few or no rights, and unless they found another man to marry, were in a dangerous position.
3.) Why do we more frequently talk about Jesus and Mary, but leave out St. Joseph?
Who’s this “we” you speak of? I talk about St. Joseph all the time. I say daily prayers to him. I constantly ask him for his help and protection. St. Andre Bessette initially inspired me to do this but I have found plenty of encouragement along the way.
4.) Are there any approved apparitions of St. Joseph?
Yes. He appeared at Fatima, a Vatican approved apparition, on Oct 13, 1917, holding the Child Jesus, along with Mary of course.
He also appeared in 1519 at Cotignac, France as part of the Our Lady of Graces apparitions, which were traditionally approved (there was no formal approval process then) and pilgrimages have been conducted to the site for years.
In addition, the reported apparitions of Joseph (and Mary) to Sister Mary Ephrem, the “Our Lady of America” apparitions in Fostoria, Ohio and Rome City, Indiana, have been approved for faith expression by the Archbishop of Cincinnati. I do a First Wednesday devotion to St. Joseph that was promulgated by Sister Mary Ephrem. (It’s nothing big. You go to Mass, receive Communion with the love that Joseph had in his heart for Jesus, and then you say the Joyful Mysteries rosary meditating on it from St. Joseph’s perspective.)
I will answer your prayer question in the next post as this is getting quite long…