Learn Turkish: Hamile kadın boşanıyormuş. - I heard the pregnant woman is getting divorced.

It combines the present continuous suffix -ıyor (is doing) with the hearsay/inferential suffix -muş (I heard / apparently). Together, they express an ongoing action that you learned about from someone else or gathered from evidence.

Could boşanıyormuş also mean 'I heard she was getting divorced' in the past?

Yes! Depending on the context, the combination -ıyormuş can translate to either 'I heard she is doing it' or 'I heard she was doing it'. Without past-tense time words in this sentence, it naturally defaults to the present.

Why is kadın translated as 'the pregnant woman' if it doesn't have a specific accusative suffix?

In Turkish, the subject of a sentence is always in the bare (nominative) form and never takes the accusative suffix. Because it doesn't have the word bir (a) in front of it, which would make it hamile bir kadın (a pregnant woman), we understand it as specific.

What is the exact base verb for boşanıyormuş?

The base verb is boşanmak (to get divorced). You might also see boşamak, which means to divorce a specific person. The -n makes it reflexive or reciprocal, which is the standard way to say a couple is separating or someone is going through a divorce.