Learn Turkish: O yorgun adam televizyon izliyor ve esniyor muydu? - Was that tired man watching television and yawning?

The past continuous question is made of the continuous ending -iyor (doing) plus the question particle mu and the past tense marker -du (was). Because -iyor always ends with the vowel 'o', 4-way vowel harmony dictates that the question particle must take the 'u' form. The 'y' is a buffer letter to separate the vowels. Therefore, "was he doing?" is always -iyor muydu.

Why isn't there a muydu after izliyor as well?

In Turkish, when you list multiple actions happening in the exact same tense for the same subject and connect them with ve (and), you only need to put the final tense and question markers on the very last verb. The muydu at the end of esniyor applies backward to izliyor as well, saving you from repeating it.

The verb for "to watch" is izlemek. Why is it spelled izliyor here instead of izleyiyor?

When a verb stem ends in a vowel (like the 'e' in izle-), that vowel is dropped or narrowed when we add the continuous -iyor ending. So, izle- loses its 'e' and combines with -iyor to become izliyor. You can see the exact same rule happening with the second verb: esnemek (to yawn) loses its 'e' to become esniyor.

I learned that means "he", "she", or "it". Why is it translated as "that" here?