Learn Spanish (Latin America): Habiendo hecho eso, el demandante no apeló. - Having done that, the plaintiff did not appeal.

The perfect gerund (habiendo + past participle) is used to show that one action was completely finished before the main action happened. If we used the simple gerund haciendo (doing), it would sound like the plaintiff didn't appeal while in the middle of doing it. Habiendo hecho eso clearly sets up the timeline: first they finished doing that, then they chose not to appeal.

Does el demandante mean 'the demanding person'?

Not in this context. In legal contexts, el demandante translates to 'the plaintiff' (the person who brings a lawsuit against someone else). It comes from the verb demandar, which can mean 'to demand' but frequently means 'to sue' or 'to file a lawsuit' in the legal world.

Why do we use the neuter pronoun eso instead of ese here?

Eso is a neuter pronoun used to refer to an abstract concept, a general situation, or a previous statement or action, rather than a specific masculine noun. Because 'that' refers to the unnamed action the plaintiff just did, we use eso. If 'that' referred to a specific masculine object, like a document (ese documento), we would use ese.

Why is the main verb apeló in the preterite tense?