What are my punctuation options here:
He said: «When will you come?» or: «When will you come»?
How else can I punctuate that sentence to the standards of the German?
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Because the direct quote is a complete sentence in your example, the question mark is placed inside the quotation marks. So your first version is the right one. However, since you are explicitly asking about the standards for Berlin, in Germany: Outward-pointing guillemets are quite uncommon in Germany (though normal in Switzerland). You would either use them inverted, or use different quotation marks instead:
Er fragte: »Wann kommst du?«
Er fragte: „Wann kommst du?“
About this see also What is the correct way to denote a quotation in German?
If, on the other hand, the quoted part isn’t a complete sentence and the question mark logically belongs to the outer sentence, it is placed after the closing quotation mark:
Ist er an Bord der „Sonnenschein“?
(Here, Sonnenschein is presumed to be the name of a ship.)