How can ´ring´ and ´steal´ be the same verb? No logical connection at all.

and "to play" too

radyoda arabesk bir şarkı çalıyor...

Does it have to be a logical connection for eşsesli kelimeler?

The cliche example, yüz means:

• a hundred
• face
• to swim (root of yüzmek)
• to skin (take the skin from body)

How should we try to catch the ´connection´ between these words?

Çalmak also means vurmak "to hit",  as you can see in the sentence "al da başına çal" 

Also there is another meaning of çalmak let me explain it with and example: "onun gözlerinin rengi yeşile çalıyor"  means color of his eyes is not exactly green but something similar to green  

So there are many different meanings of this word.  I think you are right there must be connection between them but I don´t know what it might be. 

Çalmak also means vurmak "to hit",  as you can see in the sentence "al da başına çal" 

Also there is another meaning of çalmak let me explain it with and example: "onun gözlerinin rengi yeşile çalıyor"  means color of his eyes is not exactly green but something similar to green  

So there are many different meanings of this word.  I think you are right there must be connection between them but I don´t know what it might be. 

Yoğurt çalmak . may mean "stealing yoğurt", but also means putting yeast into milk to turn it into yoğurt.

HER TELDEN ÇALMAK    ?

same reason how "on" can mean, "on top of" and "turned on" and "on the track of" and "on a problem" and "on the phone" and "on the internet" at the same time

I also think it is not coincidental: one syllable verb roots hardly just lapse together.

One possible explanation is foreign influence. The corresponding verb in Arabic or Persian may have a range of meanings and these may have been transferred from language to language by bilingual speakers.