I don't have a huge problem with the backstory, but I am going to point out the elephant in the room;

The gun.

Simple question is; why? You can't have a gun casually in Japan. Perhaps for hunting, but I can't imagine how difficult it would be for a foreigner to get through all the red tape for a permit. You suggest it's precious to your character, but you haven't gone into why in your very limited backstory, which gives the impression you just added it for something "cool" to have. Not to mention you wouldn't get to use it in a combat situation since your character seems to not be a Persona user and thus not someone that will be encountering any situation where a weapon, let alone a gun, would be necessary. Even if you were, I'm not sure I like the idea of a gun being used in a Persona RP. It just seems out of place.

If you can come up with a intriguing reason as to why he should have a gun, I'm all ears. But as it stands, I don't think it's either necessary nor worthwhile to have.