Learn Dutch: Geregisseerd door haar vader, speelde de actrice de monoloog perfect. - Directed by her father, the actress played the monologue perfectly.

In a past participial clause (abridged clause or beknopte bijzin), the subject is omitted. The golden rule is that the implied subject of this clause must be the same as the subject of the main clause. Here, that subject is de actrice. If the sentence ended with something like was de monoloog perfect, it would be grammatically incorrect because a monologue cannot be directed by her father!

Why does the second part of the sentence use inversion (speelde de actrice instead of de actrice speelde)?

The entire participial clause (Geregisseerd door haar vader) acts as the first "block" of information in the sentence. Because Dutch follows the V2 (verb-second) rule, the main verb speelde must immediately follow this first block, pushing the subject (de actrice) to the third position.

How does using a past participle (Geregisseerd) change the meaning compared to a present participle (Regisserend)?

A past participle gives the clause a passive meaning or indicates a completed prior action. Here, it means the actress was directed by someone else. If we used the active present participle (Regisserend), it would mean the actress herself was doing the directing while she played the monologue.

Is this sentence structure common in everyday spoken Dutch?