In practice, you can assume they do - it's a simplified but accurate model of reality when you're not researching the life of insects and rodents.

Yes, life does not appear "out of thin air", but it constantly tries to get in, will exploit any crack in your defenses or attention to chase after anything that looks or smells like food or safety. It's simpler to just assume annoying critters materialize out of thin air if you leave the right conditions, and ensure those conditions are never present.

It's kind of like thermodynamics / statistical physics: the air around you doesn't really have "pressure" or "temperature", but you may just as well assume they're a thing, since the alternative would be to talk about kinematics of air molecules.

We had no mouse problems that winter, and very few since then.

I see that as realistic, if we are talking 2D spaces. In urban environments, they live in sewers, and you have sewers under every building. In the countryside, they obviously live everywhere.

I can see that 6-metres rule broken only if going 3D, i.e. in multi-storey buildings with spotless maintenance of any nook and cranny, living on the third or fourth floor, you might be a bit further away than that.