Mechanics of Clara's "Impossibility"
Clara upon entering the Doctor’s timeline (or corpse, depending on your point of view) is splintered in time. What we see (and have experienced to date in S7) is not one Clara at multiple events, but many individual Claras born in different points in time and unaware of each other.
Clara-Prime (the original Clara, though the 3rd we’ve met. Timey-Wimey) by stepping into the timeline on Trenzalore is splintered. Thus there are multiple Claras born in multiple timeperiods, including the Victorian era. The Victorian era Clara helps The Doctor and dies.
Now for us to continue, you have to wrap your head around the fact Victorian Clara is a COMPLETELY DIFFERENT PERSON than Clara-Prime. Are we on the same page?
Clara-Prime also splinters into Oswin from Asylum of The Daleks. She is also a COMPLETELY DIFFERENT PERSON than Clara-Prime and Victorian Clara. She also dies helping The Doctor.
So the premise you need to walk away from, the concept that needs to be understood, is that what makes Clara “Impossible” is that she is born in multiple timelines. Born of different mothers. Different lives, but compelled to help The Doctor in each.
That’s why The Doctor is intrigued, mind you.
He’s met the same person in different historical eras (i.e. River Song). There’s nothing impossible about being in Victorian England and in a Starship named Alaska (at least not in the Doctor Who universe).
What made Clara impossible is that there were “copies” of a woman scattered throughout time, splinters. All people are born unique, but here was one person born over and over again, who was not.
So, if we agree on this, then I can share with you my insight on 'The Name of The Doctor'.
An insight that is potentially more mind-blowing than Hurt revealed as an unknown incarnation of a past Doctor.
We agree that all the Claras we have observed in ‘The Name of The Doctor’ are not a single Clara travelling in time, but rather many different Claras.
Different Claras, born in different timelines, waiting to meet The Doctor (the way Victorian Clara is a different person than Clara-Prime and Asylum Clara). The Clara that chases after the Second Doctor IS NOT the same Clara that yells for the Third Doctor.
So who is the Clara who tells The First Doctor which TARDIS to choose?
They’re on Gallifrey!!
Gallifrey, during a period where humans were not allowed on Gallifrey (see Doctor Who: The Deadly Assassin).
Clearly, the only assumption that can be drawn is that ... A VERSION OF CLARA WAS BORN ON GALLIFREY!
A Clara-Splinter, born on Gallifrey.
Think about it …