Hi me,
Welcome. I doubt that you'll find the answers to the questions you seek. The thing about ancient historical accounts is that you only get what has been passed down in the actual evidence. Questions regarding issues that have not been preserved in the evidence are not going to be answered with any assurance that they are the truth, but one can always ask.
You wrote:
If the three wise men truly were wise, why did they not foresee that a despot such as Herod would seek the death of Jesus?
Since they were strangers to the land of Israel, there really isn't any reason that they would have known the nature of Herod. We know it today because we have the Scriptures to tell us the things that he did. They didn't have that resource. I'm not really sure that the things that Herod did prior to the time of Jesus would have been considered particularly heinous of rulers of that day. There are many accounts of questionable actions by the various kings and rulers that lived 2,000 years ago. Communication wasn't as instantaneous as it is today.
Finally, being wise doesn't mean the same as being omniscient. However, one needs to also consider that there were prophecies written about Rachel weeping for her children. That prophecy could only come to fruition if Herod did what Herod did. That prophecy could only come true if Herod found out about Jesus' birth. Perhaps those wise men were wiser than you're giving them credit for.
What were the ages of Joseph and Mary at the time of the conception?
Don't know and don't really see any reason that it might matter in any way. They were whatever age they were.
You asked:
When Mary was found to be "pregnant by the Holy Ghost," who found her thus, and how? Who was informed of this, and to what extent?
By the evidence of the Scriptures we know that the angel knew and I imagine he knew by way of God who sent him to visit Mary. Based on Mary's response, I'd imagine that she didn't even know that she was pregnant at the time she was told. We know that Joseph knew because he considered divorce because of that very issue. We know that a time came when Elizabeth knew. Beyond that it would all be a guess as to when and how others came to know that Mary was pregnant. I would also imagine that under the circumstances of the nature of her pregnancy that it wasn't something that was widely known. Mary would have been widely shunned by people if they knew and there isn't any evidence that she was. It's likely why she went to another town for awhile. However, all of that is merely guesswork and supposition. As initially mentioned at the top of this post, we only have the evidence that we have and any answers for questions outside of that evidence is purely guesswork.
How does Joseph "being a just man" square with him contemplating a coverup?
We all run possible actions and outcomes through our heads when faced with tough situations. It's natural and I can't imagine that such a practice of considering different options and actions to cause one to be considered 'unjust'. Now, to follow through on one particular action or course that is an unjust course, would be unjust. However, humanly speaking, Joseph would still have been a just man if he had sent her away. That's why God sent the angel to Joseph. To give him insight and understanding of what was happening.
Why is there not even a mention of Mary's experience of having the future Son of God within her womb? Presuming that she knew what unborn child she carried.
You mean like one of the gospel writers writing that there was a day that Mary said, "Ooooh, I felt the baby kick."? She had been told 'what unborn child she carried'. Her knowing that she hadn't had any sexual relations, - after all Mary knew the things she had done whether she told anyone else or not, she knew the truth of her own actions, - would certainly indicate to me that she knew that there was something special about her child even without the knowledge given her by the angel. Let's be real here for a moment. A woman who knows that she's never had sexual relations comes up pregnant? It's not like people didn't know what caused pregnancies in those days.
So, all questions for a mind to ask, but expecting any sure truthful answer to such thoughts should be understood by anyone as highly unlikely. We can only answer the questions for which we have some evidence with which to know the answers. All we can know is that Mary and Joseph were real actual people who lived in Israel in that day and they were, therefore, some age. We don't have a clue, based on all available evidence, what that age was. We don't have a clue, beyond the people we are told who knew that Mary was pregnant, who knew that Mary was pregnant or had any idea the circumstances under which she became pregnant. We know that Joseph was considered to be a just man because the Scriptures tell us that he was. Personally, that's ample evidence for me that Joseph was a just man whether you or I would agree or not. Ultimately, the Scriptures tell us that he did do the just thing. There's no further mention of the day to day activities of Mary throughout her pregnancy and so all we know is what we've been told.
We are cautioned against going beyond what the Scriptures tell us and I honestly can't find any reason why we need to know any of these answers. In what way might it matter if Mary was 15 or 30? In what way might it matter if we were told of every minute of Mary's life from the time she was told that she was with child until the birth?
God bless you and welcome again,
In Christ, Ted