Really a general ruling: Is it true that I can use garth's ability

pay 3 end -> get a card from discard //paraphrased

while he's exhausted?

Brian

yes,..as long he is not stunned you may put his ability on the chain.

he can be exhausted or not, and you dont have to exhaust him to use the ability.

In general, unless an ability specifies 'Activate' in the cost, or specifies in the effect that the character needs to be ready in order to use it, you can use the effect at any time.