Learn Russian: Сообщают, что звезда уже родила дочь. - They report that the star already gave birth to a daughter.

This is an indefinite-personal clause. By using the third-person plural verb сообщают without a subject, the sentence expresses that someone is reporting this, but the specific identity doesn't matter. It translates well to the passive 'It is reported' or the general 'They report' in English.

If I added the word Они to the beginning, would it mean the same thing?

Adding Они changes the focus. Они сообщают means a specific group of people who were already mentioned (like a specific news team) are reporting it. Leaving it out keeps the focus on the general rumor mill or media.

Дочь is the direct object of the verb родила, so why doesn't it have a typical accusative ending?

It actually is in the accusative case! Дочь is a third-declension feminine noun, meaning it ends in a soft sign (like ночь or вещь). For these nouns, the accusative form is exactly the same as the nominative form.

Why does the word уже (already) pair with the perfective verb родила here?

Уже highlights that a result has been achieved by a certain point in time. Because the action of giving birth is a completed, one-time event resulting in the daughter being born, the perfective past tense родила is the correct choice.