Question with #4.

Is the ´i´ in dediğini the object marker?

I´m a bit stuck on "-dik". I don´t know if it is present or past. I saw this in another thread: güldüğünü biliyorum - i know that you are smiling. How do we know that it isn´t "I know that you were smiling" or "I know that you smiled"

Yes, it is object marker for the verb -anlamak .

What did I not understand ?

I did not understand "what you said "

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Note that to prevent confusion whether it is "what you said" or what he/she said", "senin " or " onun " can be put in the begining of the sentence.

Senin ne dediğini anlamadım.

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Past/Present  -dik  carry both tenses though [past - present]

 So we need the whole context to decide.

Güldüğünü biliyorum. --> I saw that you laughed /smiled.

                                     I saw that you are laughing / smiling.