"Stamina Thief - Increases certain attacks' ability to exhaust monsters." Which attacks exhaust monsters? is it weapon-specific? Power attacks? etc.?

apart from bowgun ammo and exhaust phials, the hunting horn will do great exhaust damage. Hammer does KO while HH does uxhaust, so definitley skill in stam thief to a horn build if you can! to fully answer your question though, exhaust damage will
come from discharge attacks used in sword mode with an exhaust phial, using exhaust ammo, and to my knowledge using hunting horn in general as long as your hitting the head or legs

What does this even mean??

Monsters have an invisible "stamina gauge" that is drained by exhaust attacks. Once that gauge is depleted, the monster begins drooling and may stand still, move slower, or be unable to use certain attacks, e.g, Rathian failing to shoot fire. Blunt weapons like Hammer and Hunting Horn deal both Stun and Exhaust, Hammer specializing in Stun and HH in Exhaust. Some other attacks like environment damage, staggers, breaks, tail cuts, and knocking out of the air may also deal exhaust damage, but you may not see the monster actually become exhausted if you're not using a blunt weapon.

So only hammers and hunting horns deal standar exhaust damagae?? I want to deal exhaust damnage with my gunlace but i don't know if it'll work or not

The Drain Jewel grants Stamina Thief.

Do charge blade impact phials cause exhaust damage?

Exhaust damage is a sub-category of Impact damage ;
Impact damage to the head will do KO damage, Impact damage to the rest of the body deals Exhaust damage.
Also, breaking parts with any damage type/weapon will deal Exhaust damage.
Hammers, Hunting Horns and weapons with Impact/Exhaust phials are the most common sources of this damage type.
Hope this helps.

Does the Arc shot with Bow deal Exhaust damage too?