Was Judaism Polytheistic Prior to their Babylonian Captivity, and also, how was Judaism influenced by Zoroastrianism?

Was Judaism Polytheistic Prior to their Babylonian Captivity, and also, how was Judaism influenced by Zoroastrianism?

I read that when the Jewish people were liberated around 537 BC from Babylon, they were influenced by Zoroastrianism to become monotheistic, which surprised me.

• How was Judaism influenced by Zoroastrianism, and were they polytheistic before this?
• It seems that the Jewish people always had a knowledge or awareness of the ancient Persians from Cyrus the Great onwards. Also, Jesus was visited by 3 Zoroastrian priests called Magis when he was born. Was there any interactions with ancient Jewish people with ancient Hindus/Buddhists?