I updated my OP with new findings re: explosives and martial abilities.
i assume power levels do not work with martial abilities/lashes? For example if i have +X to fire power leves it doesn't make my flames of devotion stronger or +X to electricity doesn't make swift strikes stronger?
So I did some test and power levels do work with martial abilities, both weapon-based and non-weapon based (thanks Alhoon for the tip-off!).
So +x to fire power levels will make flames of devotion stronger (assuming it is appropriately tagged).
Lash damage will be boosted insofar as the base damage of the weapon gets adjusted upwards from power-level scaling (or via Empower). However, most lashes I see are pretty low (15-20%) so don't expect too much extra lash damage from even an Empowered ability.