Your instincts were correct on the first sentence:
He (pronoun subject) treated (verb) them (pronoun direct object) badly (adverb modifying treated).
The passive construction is:
They were treated badly by him.
Your next two sentences demonstrate restrictive and non-restrictive relative clauses.
A) The accusation that the actor dismissed his agent is laughable.
B) The accusation that the actor has dismissed is laughable.
In sentence A the phrase "that the actor has dismissed his agent" is attached to the word "accusation" and without that phrase the sentence would lose most of its meaning. This is a restrictive relative clause.
In sentence B the phrase "that the actor has dismissed" is additional information about the accusation and is not necessary for understanding the meaning of the sentence and is therefore non-restrictive and should be set off with commas:
B) The accusation, that the actor has dismissed, is laughable.