Affinity on weapons

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.

Khezu was somewhat notorious for hugging the ceiling in MHFU, and that doesn't seem to have changed. It is not usually an efficient fight as a Blademaster. Unfortunately neither sonic bombs nor flash bombs have any effect on Khezu.

Dung bombs act as usual and may get Khezu to leave the area (which might mean he's not on the ceiling of the next area). Felvine has no effect on Khezu.

I think your options are:

1. Switch to a ranged weapon, or hunt online in a party with at least one Gunner.
2. In some areas it may be possible to jump off a ledge and just scrape him with your carving knife (you may even be able to mount if you're lucky/he's in the right place). Bugstaff is good for this because of the pole vault manoeuvre. There is a big pillar in Area 5 of the Frozen Seaway which is good for jumping off. Further, the walls in Area 6 and cliff faces of Area 4 are also effective for climbing up (usuallu Khezu will walk near you if you are up the top of a wall while it is on the ceiling) and after a few whacks you can knock it off, for a knockdown and often a shiny drop. Note that getting it to fall off doesn't seem to be as difficult as triggering a regular flinch.
3. Make additional bounce bombs (especially bounce bomb+ if you have Bomb Arrowana) and try to hit Khezu with enough of them to make it flinch.
4. Stand still while Khezu is on the ceiling, in the hope of provoking it to attack you. Then dodge. Try this directly underneath the Khezu when possible.
5. Dung bomb him and hope that he leaves soon and does not immediately crawl onto the ceiling of the next area.

Of course, using traps, barrel bombs, and tranqs (the latter only if you don't need carves) as well as Fire element (for regular Khezu) will speed up the fight as a whole. That won't get him off the ceiling once he's up there but should result in reduced ceiling time overall.

The best parts of Khezu to target are its Neck (cutting damage), or its Head (impact damage and shot damage).

TL;DR Sometimes being a Blademaster is inconvenient.

I am not sure if so-called constant rage mode has made a return in MH4U but if it has, I think doing more damage quickly to Khezu should help provoke this, and a nearly constantly raging Khezu should spend less time on the ceiling and more time actively trying to kill you. YMMV whether that speeds the fight up.