Learn Spanish (Latin America): Escuché a alguien vomitando en el baño. - I heard someone vomiting in the bathroom.

With perception verbs like escuchar, you can use either the gerund or the infinitive. Using the gerund (vomitando) emphasizes that the action was in progress—you caught them right in the middle of it. If you used the infinitive (vomitar), it would sound more like you heard the entire completed event from start to finish.

Why do we need the word a before alguien?

This is the personal a, which is required before a direct object that refers to a person. Even though alguien (someone) is an indefinite pronoun and we do not know the person's identity, it still represents a human being, so the a is mandatory.

If I wanted to replace a alguien with the pronoun for 'him', where would it go?

To say 'I heard him vomiting', you would say Lo escuché vomitando. The direct object pronoun (lo) goes before the conjugated perception verb (escuché). You do not attach it to the gerund in this specific structure.

Could I use a relative clause like que vomitaba instead of the gerund?

Yes! Saying Escuché a alguien que vomitaba is another very common and natural way to express this. Using que plus the imperfect tense works just like the gerund here to describe an ongoing background action that you perceived.