What are the rules (if any) on ranged weapons while flying? (I'd assume that the rules would be similar to using ranged weapons while running, but I just want to know if there are any actual rules on it.)
This question is similar, but I can't find the answer I'm looking for in it: Are there any established rules for flying in combat for D&D 3.x or d20 Modern?
Not really. Most things work normally, except for the issues that the articles in the other answer mentioned. The primary one of those being that you can't take full round actions if you have a minimum forward speed (aka: average/poor/clumsy maneuverability and do not have Hover). Beyond that, flying is considered movement, so for combat purposes it's treated that way except when the flying rules say its not.
For ranged weapons specifically, altitude differences should also be factored into your range increments. After all, if someone is directly 50' above you, they're not in the same square! (A table here mentions that issue, squares while flying are 5x5x5 cubes.)
Unfortunately, calculating those distances accurately in three dimensions isn't all that simple. If you want an accurate measure, you can use the Pythagorean theorem. That is, if an enemy is 25' away horizontally and 20' above you, the distance is this:
x^2 = 20^2 + 25^2
x^2 = 400 + 625
x = sqrt(1250)
x = 35.355339 (so 35 after rounding)
You can imagine how doing that at the table would get tedious pretty fast, but I'm not aware of any rule they came up with to simplify it in three dimensions.
(If you find the flying combat rules overly difficult, KRyan made a set of variant rules that address this and several other complexities of flying which might be of interest.)
