What is the mechanic behind status effect application in MH4U
Solution 1:
Since you're talking about Bows here, let's make this Bow-specific.
Yes, all damage (raw, elemental, status) is affected by the Bow's "sweet spot" range. Being in the perfect range will increase all inflicted damage by 50%. Hitzones do matter, so you'll want to target the same hitzones you normally do rather than fire willy-nilly. And yes, number of hits does matter for apply status. While the Monster Hunter damage formula is certainly convoluted and arcane, RNG does not play a factor outside of determining whether you made a critical hit with Affinity. Speaking of CritStatus works similarly to Affinity in that it gives a percent chance of dealing increased damage.
There really aren't any tips for inflicting status outside of what you would normally do. Perhaps if you dedicated to statusing, bring some extra combo materials. Other than that, just do what you normally. Note that if you get lucky with crits and hitzones, inflicting the same status twice is usually where diminishing returns kicks in, it'll be much harder to get that third status inflicted.
Solution 2:
I mained bows through most of MH3U and I doubt much has changed in 4U.
Does this "status damage" you've accumulated also decay over time when not hitting with status-inflicting attacks? If so, does it decay steadily, or does the accumulated status damage just reset after the target does not get hit with inflicting attacks for a certain amount of time; and is this decay rate/reset timer speed negligable, moderate, or very quick?
It does decay over time, yes. The best time to start applying status is when a monster just entered an area (so it's unlikely to leave it soon) or when you can get off a lot of shots in quick succession without being interrupted. The accumulated damage only "resets" after you pass the threshold and the status is applied.
It's not a fast timer but if you wait too long even the 20 shots won't be enough. Most of the time I get the status after about 12 shots, but if there's a large gap in the middle of it (around 3-5 minutes), even firing the remainder of the 20 afterwards doesn't always work.
Does the amount of status damage per hit (i.e. potency) scale with the amount of damage done by the hit? (e.g. Would a Rapid Lv1 at perfect distance apply more status damage than a Rapid Lv1 fired from too far away?) Does the potency scale with monster hit zones? (e.g. would a Rapid Lv1 to the face apply more status damage than the same shot to the body) (outside of damage also scaling with hit zones, if the answer to the previous question is Yes)
Yes, the same as everything else. Note that some monsters are more resistant to certain statuses than others, and there might be a few that are weak to status in one area but otherwise don't take much damage there. Check your weakness tables for more information.
As it pertains to Bows; is status damage applied per shot, or per hit? (e.g. Would a Spread Lv3 with 5 hits apply more status damage than the same Spread Lv3 with 1 wiff and 4 hits?)
Yes, which is the reason why focus/wide arc shots are popular for applying status, since they hit many times.
Does the poison status effect deal a static amount of damage, or does it scale with something such as weapon damage or monster HP? It seems silly that a poison effect would do the same amount of damage on a G.Jaggi as it would on say, Gore Magala.
As far as I know it's either a percentage or a set number for each monster -- I know poisoning Duramboros was a popular strategy due to its huge amount of health.