Question

Will Thunder Wave be able to hit abilities such as:

• Lightning Rod
• Volt Absorb
• Motor Drive

If so, how much HP would Volt Absorb recover?

Answer 1

Genreation I - III

Thunder Wave is unaffected by Volt Absorb. Others are affected.

Generation IV

Thunder Wave now can't affect Pokémon with Volt Absorb or Motor Drive. Lightningrod is affected.

Generation V

Thunder Wave now cannot affect a target with Lightningrod.

Source: Bulbapedia's page on Thunder Wave

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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.

Answer 2

Nope T-wave is a electric move so it won't effect those pokes.For the second part of your q 1/4 HP will be recovered.

Source