Condition Extending Mods

Do they only apply to conditions applied by the weapon, or do they apply to any conditions you inflict?

For example, if I have a Cruel mod on a bow I'm wielding and I cast Phantom Pain on a monster, will the cruel mod make it last 33% longer?

any conditions that you inflict. it doesn't have to be inflicted by a skill that is particular to the current weapon you are wielding. so yes to your example.

Bows do not have a Cruel String available. But if they did, the deep wound would last longer from Phantom Pain. One reason I put a Barbed mod on my Necro's spear for when I weapon swap. Means I don't have to swap back to use my bleeding skills. They key point is that the weapon has to be equipped when the skill is used. So if you cast Phantom Pain with a wand, and switch to a Cruel Spear/Axe/Sword/Hammer/Daggers before it ends and the deep wound is applied, it won't extend the duration. But if you have the Cruel weapon equipped when you cast Phantom Pain, the deep wound will be extended even if you swap weapons before it ends.