Learn Turkish: Geçerli bir gerekçe göstermiş mi? Niyetini hiç sezmedin mi? - Has he provided a valid justification? Didn't you sense his intention at all?

The -miş suffix here functions a lot like the English present perfect tense ("Has he provided?"). It also carries the feeling that the speaker is asking about an event they didn't personally witness, checking on the outcome: "Did it turn out that he provided a reason?" Using the simple past gösterdi mi would mean a more direct "Did he provide (at that specific moment)?"

What are the two '-i' suffixes at the end of niyetini?

The first -i is the third-person possessive suffix, making it niyeti (his intention). The second -i is the accusative case marker, which is required because "his intention" is the specific direct object of the verb. The -n- in the middle is a buffer letter that always appears between a third-person possessive suffix and any case marker.

Why does the Turkish sentence use göstermiş (has shown) for "has provided"?

In Turkish, you don't typically "give" or "provide" a justification; you "show" it. Gerekçe göstermek (to show a justification) and sebep göstermek (to show a reason) are standard collocations you will hear constantly.

Since this lesson is about 'demek ki', how might we naturally use it to follow up on this sentence?

Demek ki means "so, it means that..." or "I gather that..." and is used to express a logical deduction. If the answer to these questions is no, you could make a deduction and say: "Hayır. Demek ki asıl niyetini gizlemiş." (No. That means he hid his real intention.)