Dear Learn,
Well, we are all still learning from God's word. It is the main textbook in the school of the Holy Spirit.
Rather than answering each question specifically as they relate to prophetic types and shadows, I would like to encourage you in the spiritual significance of the stories that you referenced, as they relate to our lives today.
Of course, you are probably well aware that the Holy Spirit must illuminate the scriptures to us. But in the case of your three questions in particular, it seems that you are asking about why God took such a long time getting around to fulfilling His promises. I'll give just two reasons, and maybe somebody else wants to add to them.
1. Throughout the Old Covenant, God was revealing types and shadows of the true, who is Jesus Christ. The timing for God to fulfill His promises were just as important as the promises. Every detail revealed something, and timing was no exception.
2. Not only was timing important to fill all the details for bringing about God's promises, but also waiting on God seems to be the ultimate test for the hearts of His people.
A. When Abram and Sara grew tired of waiting on God, "Sara thought." (Gen. 16) Their lack of patience on supernatural God led them to natural thinking, and that produced a natural enemy of God's promised seed that continues to bite at their heels to this very day.
HOW MANY TIMES HAVE WE TURNED TO NATURAL THINKING RATHER THAN WAITING ON SUPERNATURAL GOD? OH, HOW MANY ISHMAEL'S HAVE WE CREATED IN THE TENTS OF HAGAR? HOW MUCH DAMAGE HAVE THEY DONE? OH, LORD TEACH US TO WAIT!
B. When the sun bore down hard over the course of time... days, weeks, months, and years in the desert - the hearts of God's people were tested. Many of them complained and were destroyed there. They wanted to either go back to Egypt, or to form another god who would not hold them accountable for their actions. Then they could fulfill their own pleasures. Ultimately, it was through that testing time that God sifted the crowd down to only those who "believed."
HOW MANY TIMES HAVE WE BEEN DISQUALIFIED FROM SOMETHING GOD HAS CALLED US TO DO, ALL BECAUSE WE WERE TOO LAZY AND SPOILED TO "FORSAKE THE PLEASURES" OF THIS WORLD IN ORDER TO MAKE THE LONG, DIFFICULT JOURNEY WITH GOD? OH, LORD! HELP US TO CAST ASIDE OUR PLEASURES NOW SO THAT WE ARE WILLING TO GO THROUGH THE DESERT AHEAD.
C. As for Joseph, the years between his dream and the fulfillment were many and long, for sure. Throughout those years, however, God's work in the hearts of His people was done. Joseph had many years to humble himself so that he would be of the right spirit to serve God well when famine came; and His proud brothers had years to recognize that their strength and pride would not provide for them when God Himself cut them off. God also corrected their attitude toward their younger brother, who they hated.
HOW LONG MUST WE ENDUE TRIALS LIKE JOSEPH DID IN ORDER TO READY US IN HUMILITY TO SERVE GOD TO THE FULLEST? OR HOW LONG MUST WE BE ALLOWED TO RUN LIKE A WILD ANIMAL IN OUR OWN PRIDE BEFORE WE HUMBLE OURSELVES TO BOW BEFORE GOD FOR HIS AID IN THE TIME WHEN HE BRINGS THE WHOLE WORLD TO A PLACE OF GREAT NEED?
Brothers and sisters! Let us not keep rushing God. A thousand years is as one day to the Lord (II Peter 3:8) Just look at all God does in us and through us when we are put in a position to wait on Him; and yet His timing is perfect. It is an essential part of fulfilling His whole will.