I'm warming up to Capaldi (Dunno how to number him, what with the War Doctor lurking anomalously in the list somewhere,)
He's 12. The War Doctor doesn't have a number. He's just the War Doctor. He didn't even think of himself as the Doctor. One of the first things he said after regenerating (maybe THE first thing - I'd need to watch Night of the Doctor again to say for sure) was "Doctor no more".
After all, she is the Impossible Girl. She tore herself apart and flung herself into his own time stream
That time stream ended at Trensalore. By convincing the Time Lords to give the Doctor another regeneration cycle she changed it. His grave isn't at Trensalore anymore and thus neither is the time rift she threw herself into. And certainly she wouldn't have interacted with any incarnation later than 11, as that was HIS grave she visited.
did the Doctor forget that she's literally a Viking's daughter, daughter of a raider, who made his living sailing over the water to that which belonged to other people?
That particular historical stereotype is inaccurate. The Vikings were no more warlike than any other peoples of that period of history. Which is to say they were plenty warlike, but they didn't go around raiding villages willy nilly.
if Sontarans live that long.
They don't. 20 is absolutely ancient for a Sontaran. Strax is already well past middle aged and quickly approaching venerable.