Keloğlan says to his mother (I am sure, I listened to it many times):

                    Ben daha çocuk. Benim yaşımdakiler sadece oyun oynuyorlar.

What happened to the personal ending? I would say Ben daha çocuğum. I thought Turkish is quite strict about subject-predicate agreement.

Yes but no so strict. Sometimes you see this kind of things. Still when a non-native speaker says such a thing it would be considered bad Turkish. When a native says such a thing it would be considered trying to sound themselves a bit different. Only for natives.

For example:

Ben anlamaz ( = "I" doesn´t understand; name of a song by Moğollar)

This is exactly the kind of mistake that I often make (because in my native language the copula is different). But ok, no handicap for foreigners.

Thanks, si++.

I am not sure but it seems he reflect a reality. his idea not just his idea, it is common or someone´s. He emphasizes his childness using from the third person mouth.

I just felt that.

This is very very detail and extreme example. Yo will never need to know that kind of sentence.

...setting back his language skills in order to be treated like a child which he actually was. Makes sense.