Learn Italian: Riposando molto, la stanchezza va scomparendo. - By resting a lot, the fatigue is gradually disappearing.

The structure andare + gerund emphasizes a gradual or step-by-step progression. While sta scomparendo just means the fatigue is disappearing right now, va scomparendo highlights that it is fading away bit by bit over time.

There are two gerunds in this sentence (riposando and scomparendo). Do they do the same thing?

No, they serve completely different purposes. Riposando acts as an adverbial phrase explaining how or why the result happens (by resting). Scomparendo pairs with va to form a continuous verb tense showing a gradual action.

Doesn't a gerund usually share the same subject as the main clause? The fatigue isn't the thing resting!

You have a great eye! Strictly speaking, traditional grammar says the gerund should share the main subject. However, in everyday Italian, it is very common to use a gerund loosely like this when the logical subject (the person resting) is obviously implied by the context.

Is scomparendo formed from an irregular verb?

Yes, it comes from scomparire (to disappear). Its gerund is formed regularly by adding -endo, but remember that this verb is highly irregular elsewhere, with an irregular past participle (scomparso) and irregular present tense forms (like scompaio).