The book states that at the 21-60 corruption point level, you may use an Infamy point to

• The Heretic may reroll any failed Characteristic
Test, using the same penalties and bonuses as
the original Test. He must use the results of the
second roll. Only one re-roll per Test is allowed.

Does this mean that you cannot reroll skill tests, as they are not raw characteristic rolls?

Almost every roll in the game is a Characteristic Test, including Skill Tests. Skill Tests are simply Characteristic Tests that are modified based on the Skill a character has.

According to the rulebook, a Characteristic Test and a Skill Test are 2 seperate things.

A WS test to hit is a Characteristic Test.
A Dodge or Parry to negate that hit is a Skill Test.

It is further confused by the wording of
"• The Heretic immediately removes all levels of
Fatigue he is currently suffering.
• The Heretic immediately heals 1d5 Wounds, and
any Critical Damage (though the effects of any
Critical Damage or Critical Hits are not removed).
• The Heretic may add a +10 bonus to a single
Test before rolling. "

All Skills are based on a Characteristic. When a character makes
a Skill Test he is testing a Characteristic.

Copypasta'd from the corebook. You're welcome.

Every test that is in some way based on any of your characteristics you can reroll with an infamy point. Dodge? Check. Focus Power Test? Check. Repair a forcefield? Check.

What you can't reroll with an infamy point is for example Zealous Hatred rolls, Force Field rating rolls, Psychic Phenomena rolls and such things that aren't based on your characteristics.