1) How long does a stun last? Was it effective in knocking out an enemy for hours? If then, I would think they would rely on stun in most situations...
One would think this would vary significantly from individual to individual, with several parameters affecting the outcome:
- State of health
- Armor or other clothing
- Exposure (standing out in the open; half of torso obscured; completely behind foliage; etc.)
This may be why stun is definitely an option in warfare (Kirk and Spock use it in "Errand of Mercy"), but only when you have good intel on your homogeneous target.
For shortest recovery, I think LaForge in "Samaritan Snare" might qualify - it was possibly a matter of minutes, but cuts in the action clouded the issue. For longest, there are explicit stun fatalities in ST6 (Burke and Samno), and an implicit fatality in ST3 (Kirk fires an odd-looking pulse at the Klingon extra after reaching Kruge's camp)...
2)Why, on DS9, did they often seem to fire their phasers on the lethal setting (e.g. against the Klingons in "Way of the Warrior"; against the Jem'Hadar whenever they encountered them) and blow up enemy ships
Apparently, stun is easy to shield against, so it never works against starships; disabling, non-lethal shots with lethal weaponry in turn are almost impossible to achieve if the target is resisting.
But the ground troops? Well, one does hope the cumbersome "armor" worn by Klingons, Cardassians and Jem'Hadar does some good. It is established not
to stop kill phasers or sharp objects or even help against punches and kicks - but perhaps it stops stun blasts cold (despite always lacking a helmet or other head protection component)?
One would think Kor's guards in "Errand of Mercy" would have been wearing stun-stopping armor, though. Granted, the "chainmail" or "fishscale" vests of the era aren't cumbersome and thus might defend their role as mere affordable decoration - but in the wider Trek context, Klingons have been dealing with stun blasts for centuries before TOS, and have been witnessed wearing cumbersome padding in the 22nd century already. Perhaps the TOS smoothheads were a special kamikaze unit that chose to fight unarmored as an extra sign of courage, to offset the shame of their mutated faces?