Re watching Tennant's episodes and one thing that I'm questioning, the Doctor stated at the start of the episode that the TARDIS will take care of the backstory for John Smith etc.
Was there a reason that 1913 was chosen? Given the Doctor's personality and aversion to violence it's not the best of hiding spots and it's more likely he'd do something out of character as it's shown fairly early on that he still has part of his Time Lord personality and memories.
The episode was adapted from a 1995 novel "Human Nature" by Paul Cornell. The book was originally a 7th Doctor story. Out of universe, the choice of location and time period was really driven by the plot of the novel, not the TV show.
The plot of the novel is that The Doctor takes a "vacation" from being himself to sample life as a human, as his companion at that time (not a companion from any TV series) was grieving the death of a character from a previous novel and The Doctor was struggling to comprehend the process. In the novel, The Doctor purchases a device which alters his biodata, but there is no mention of any backstory being created by The TARDIS.
I would suggest that the decision to leave the backstory up to the TARDIS in the TV script was just for simplicity, but in-universe it could be argued that as it is meant to have the ability to cloak and blend in, perhaps it also has the ability to conceal The Doctor? The pocket-watch device held his original personality and biometrics, so presumably it was that which made him human and all the TARDIS had to do was provide the memories as a "cloak". By contrast, The Master was in possession of the pocket-watch and presented as human but was without a TARDIS and had no memories of where he came from.
Remember also that Martha had to blend into this timeline whilst retaining all her memories. Presumably, she just had to go along with whatever The Doctor now believed. The choice of time and location would also have had to account for her and not been a time period in which either of them would stand out as unusual. Wartime may have just been a good choice because there was so much else happening at that time.
It might not have been chosen. Not really. In the old series, the TARDIS used a randomizer which meant that they never really knew where they were going. This was to avoid a specific enemy.
From what I could tell they had gone to multiple times and places to get away from the Family--it might have been like regular running--you are running away, but you don't exactly PLAN where you end up.
As far as I know there's not a canon reason for it being chosen. (But you can't prove a negative). Still, based on what I know of the Doctor's pattern when it comes to running away, most of the time he doesn't actually plan these things carefully.
You're arguing that the Doctor's aversion to violence would make him easy to spot. But if you look at the actual episode, his persona has no such aversion. While he might have stray Doctor dreams and images, he doesn't do anything out of character on that front.
Further, he isn't as adverse to violence as you might think. He's just more clever about it. He WAS the War Doctor, his name is not synonymous with peace. Put him in a war and he's actually very, very good at causing causalities. That's not an aversion to violence, that's being good at it. And that's why he tends to be careful in the series about violence, because if he does go to war, he's excellent at it. And yes, he hates that about himself, he hates that he likes it and is good at it. Just like he hates the fact that he's officer material. Danny Pink calls him on it.
