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.
It did not develop exclusively from high German, as I wrote before and it was geographically widespread enough for clear Eastern vs Western dialects to emerge:
Rather than existing "in the area we would now call west Germany" as you would like to believe for some reason. Eastern Yiddish in particular is much more than "a German language" (unless you want to call Polish a German language as well).
