1.) It is not true. You are misunderstanding two differents meanings :

• clémence = quality of being clément(e)
  

  fait preuve de clémence (he was kind this time)

• clémence = act of kindness
  

  fait preuve d’une étonnante clémence (he did a kind act in particular)

2.) clémence can be associated by kindness but also by mercy and tends to be disused. clémence may associated to the power to give death and mercy about it and there is not a lot of people who has this power actually. So it is used idiomatically and as a picture of great kindness (that’s why it is surprising nowaday (inhabituel/étonnant)).

3.) We can totally say

C’est une clémence qu’il t’a fait en évitant de parler de ton erreur.

When you add “une” before “clémence”, you make it distinguishable from others. It becomes not only a standard act of kindness but this very act of kindness.
Only saying:

Il a fait preuve d’une clémence.

Would mean he was kind in a particular way, but without saying in what this way is particular, that’s why it’s weird. Whereas saying:

Il a fait preuve d’une grande clémence.

Means he was very kind (“grande clémence”), but without making a difference with every other time someone is very kind. You loose the uniqueness.