A comma separates clauses that make grammatical sense on their own, or at least where one of them does. So "In Greece, we have a similar phrase" is fine, because "we have a similar phrase" is complete in itself. Whereas "Readable code, is a piece of code" is not correct, because "is a piece of code" is not complete - it's missing a subject. Likewise, "In Germany, they say" and "In 16th century, in the Habsburgermonarchy" are fine, but "but let me, tell you a secret" is not.

As a native speaker, i can understand those sentences well enough, but they look wrong, and i wouldn't expect a fluent native writer to write them.

I have a Greek friend who is similarly scattershot with commas (eg "Hey send me, the photo of your office!"). I wonder if this comes from mapping some feature of Greek sentence structure onto English?