Learn Turkish: Öğretmen her gün soru soruyor. - The teacher asks a question every day.

The subject of the sentence is öğretmen (the teacher), which is third-person singular (like 'he' or 'she'). In the present continuous tense, the third-person singular form is just the verb root plus -iyor. It does not need an extra personal suffix at the very end.

The translation says 'asks', but doesn't -iyor mean 'is asking'?

Yes, -iyor is the present continuous tense, normally used for actions happening right now. However, Turkish often uses this tense for habits and routines too. Because of the phrase her gün (every day), we know this is a habit, so it translates best to the English simple present 'asks'.

Where is the word for 'a' in the Turkish sentence? The translation says 'asks a question'.

In Turkish, you do not always need to use bir (a/an) for general, non-specific objects. Because the teacher is just doing the general action of question-asking, soru stands alone without bir.

The words soru and soruyor look almost the same. Are they related?

They are! Soru is the noun for 'question', and soruyor comes from the verb sormak, which means 'to ask'. Turkish often builds nouns directly from verb roots.