Learn French: L'accusation qu'il a faite n'est aucunement justifiée. - The accusation that he made is in no way justified.

This is a classic rule to watch out for: when using the auxiliary verb avoir in a compound tense, the past participle must agree with the direct object if that object comes before the verb. Here, the direct object is qu' (standing in for the feminine noun l'accusation). Because it comes before a faite, we add an e.

How does "aucunement" work here? Does it replace "pas"?

Yes, exactly. Aucunement means "in no way" or "not at all." It is a negative word that pairs with ne (here, n'), and it completely replaces pas. The sentence structure works exactly the same as a standard negative: n'est aucunement justifiée.

Could I use "pas du tout" instead of "aucunement" in this sentence?

Yes, n'est pas du tout justifiée would mean the exact same thing. Aucunement just sounds a bit more formal or emphatic. Another formal alternative you might see at this level is nullement.

Why do we use "qu'il" instead of "qui il"?