Learn Turkish: Evli çift kavga etmeden boşanıyormuş. - I heard the married couple is getting divorced without fighting.

This is the inferential present continuous (verb + -Iyor + -muş). The -Iyor part shows that the action (getting divorced) is an ongoing process right now. The -muş part shows that the speaker is reporting information they heard from someone else rather than something they witnessed directly. That is why the English translation includes 'I heard...'.

Since a couple (çift) involves two people, why doesn't the verb have a plural suffix like boşanıyorlarmış?

In Turkish, collective nouns like çift (couple), aile (family), or grup (group) take a singular verb because they represent a single grammatical unit. You only use the plural suffix on the verb if you make the noun itself plural, such as çiftler (the couples).

How does kavga etmeden translate to 'without fighting'?

It uses the suffix -mAdAn, which means 'without doing [action]'. The base verb is kavga etmek (to fight). By dropping the infinitive -mek and attaching -meden, you get kavga etmeden (without fighting).

Is the word evli (married) related to the word ev (house)?

Yes! The noun ev means 'house' or 'home', and the suffix -li means 'with' or 'having'. So literally, evli means 'with a household', which is the standard Turkish word for 'married'.