Genreation I - III
Thunder Wave is unaffected by Volt Absorb. Others are affected.
Thunder Wave now can't affect Pokémon with Volt Absorb or Motor Drive. Lightningrod is affected.
Thunder Wave now cannot affect a target with Lightningrod.
Source: Bulbapedia's page on Thunder Wave
So in Gen V, Thunder Wave has no effect on Pokemon with those Abilities.
To answer the second part of your Q, all Electric type moves recover 1⁄4 of its maximum HP when hit by an Electric-type move.