My understanding is that the Persian King would commission scholars to live in his city and he would support them in studying their culture’s wisdom. In exchange for his support, their job would be learn what they could about their culture’s wisdom and then teach the King what they learned so he would be as well rounded as he could be.
It’s entirely possible the Wise Men may have been Jewish, since they learned when and where the Messiah would be born.
Indeed. Persia had many Hebrews living in the country and we know that there were Hebrews in the palace as advisors and brides- Daniel and Esther for instance.