Learn Spanish (Latin America): Habiendo notificado al demandante, el asistente entregó la demanda. - Having notified the plaintiff, the assistant delivered the lawsuit.

The perfect gerund habiendo notificado makes it crystal clear that the notification was completely finished before the next action happened. If you used the simple gerund notificando (notifying), it would imply that the assistant delivered the lawsuit at the exact same time they were notifying the plaintiff, which does not make logical sense here.

How do we know who is doing the notifying in this sentence?

The subject of the main verb is el asistente (the assistant), and by default, a gerund clause at the start of a sentence shares the same subject. So, the assistant is the one who both notified the plaintiff and delivered the lawsuit.

Why do we need al before demandante?

Even though demandante (plaintiff) is the direct receiver of the notification, it refers to a specific person. Therefore, it requires the 'personal a'. The preposition a combines with the masculine article el to form the mandatory contraction al.

Is demanda a false friend here, or does it mean the same as the English word 'demand'?

It is a partial false friend. In economics or everyday speech, demanda can indeed mean 'demand' (as in supply and demand). However, in a legal context like this sentence, una demanda specifically refers to a lawsuit, a legal claim, or a formal complaint filed in court.