Fun fact: according to the etymology I could find online it's actually originally a German word (meaning client of a prostitute) that was borrowed by Yiddish, then borrowed in turn by Polish from Yiddish and also ended up in a couple of other European languages.
Not exclusively. It has elements from Hebrew and Aramaic (of course) as well as from various Slavic languages. A big chunk of it derives from High German but not all.
It developed from High German with elements of Aramaic and Hebrew, in the area we would now call west Germany. The only way it's not a German language is if you deny the historic and linguistic roots of the language.