[Caspian]

If I remember correctly, max damage range for gun is a little outside xbow best range, but inside bow range (hardly ever use gun anymore). Xbow is just outside of melee range, so gun range is just a little bit farther outside that. Best bet is just to play around a little with it until you find the best point. And for the most part, its pretty easy to see if your damage is going up or down based on distance.
2nd part of your question: the distance thing is basically based off of your perfect damage at ideal positioning. Based on distance, its all percentrages of 100% at the "sweet spot". Raising str and r.atk. will boost the damage in any of those positions. The rng's you see boosting those stats are, 9 times out of 10, rngs at endgame doing VT meripo parties and the like. Reason being, at that level, you don't need all the extra ranged accuracy that is usually required for a normal xp party pre-endgame. Usually the lower level rangers you see running around in str gear are doing so because thats what hi-level rangers do and they think thats is whats appropriate. There are a few cases where I'd sacrifice a couple points of ranged accuracy for many points of ranged attack, like the Shikaree Aketon for the Noct doublet +1, but thats about it (still haven't decided on food yet, since I'll be subbing WAR and don't get the extra accuracy from the offhand dagger). Really its one of those balancing games where you want enough accuracy to hit consistently, but not so much that you get too much of a diminishing return or just flat out cap it and get no returns at all.
(Honestly I haven't been able to see much of a difference in accuracy using atk food over accuracy food so far, think it was a side effect of the patch last year, but could just be my imagination)