What they did was to engage two au pairs.
What the company has done was to impose a ban.
These two above sentences are your correct ones from your examples, however I would like to offer a rephrasing for each to be more natural.
"They hired two au pairs"
"The company imposed a ban"
The reason for my more simplified changes was for two reason.
Firstly, your examples were too wordy and didn't sound so natural for everyday use unless you intend to write something like an academic thesis.
Secondly, the word "engage" can have many different meanings depending on context and when referring to people, it can imply something of romantic or sexual nature sometimes, which of course would not be good. As for your company ban sentence, it is not entirely clear whether you mean mean the ban was created by them or for them.