It all relies on one's understanding of the Bible. It is a collection of books written over about 900 years by many people from divergent communities and edited by many during the ages. Each writer and editor had their eye focused on directly influencing their own immediate community.
When recording history, for example, their purpose was to use their interpretation of history to influence their community, rather than being concerned with literal accuracy. Their records were theological history.
The NT Gospels are not intended to be a literal documentary record. They were shaped by the objectives of the original authors, employing their own local cultural understandings, idioms, language, etc.
Since each group of writers had a different background and outlook, their records differ. Each group invented the birth and crucifixion stories in a way that suited the purpose of each community. None of them was there to provide an eyewitness account of either event. Similarly with the Temptation and with Christ's baptism.
Consider the arguments that Paul's philosophising had with with the Jewish Christians' legalistic requirements. Contrast Paul's view on the Law with "no joy or tittle will be removed from the Law".
There were several disconnected NT Christian groups, often at odds with one another. For several centuries, each held on to its preferred written records until the 4th century, when the state church accepted the list prepared by Athanasius. Given his preference for Paul's philosophising over James' and Peter's Jewish legalism, this influenced the dominating list of NT books. Learn the history.
The "generations" of Jesus as given are different because they are theological lists. Look at their structure.
Regarding a "virgin" mother, I suggest that when you read the second chapter that I have provided, that you remember the chronological sequence (Paul, then Mark, then Matthew, etc).
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The reapplication of Isaiah's "maiden" of his own time into the "virgin" of the NT writers shows how they handled the Hebraic material.
We must not read the Bible through Western eyes of the 21st century. The words must be read through the eyes and ears of the culture that composed the text. It is not a technical, scientific, document but a record produced by many people. After all this, we should be amazed there is as much agreement between the books.
An interesting book might be: "The Unauthorized Version: Truth and Fiction in the Bible", by Robin Lane Fox.
Doug