Muhammad was a tradesman, and during his life, the most significant trade route went from modern day western Yemen up to modern day Syria. This was usually done with a caravan carrying supplies from the south in Yemen (which would have goods from as far away as India), the caravan would stay in Syria for 6 months, then travel south, and repeat the process in another 6 months.

What this means is Muhammad's interaction with people came through oral interaction due to him being a merchant. He had to learn (as other Arab traders had to) the people he was trading with.

Based on his teachings, he referenced many cultures. Statements like God saying "we make no distinction among them." In referring to other monotheistic prophets. Saying things like "learn from all people, even China" or emphasising how badly India needed to be freed from paganism, implies he either heard about these regions, or has been there for trade.

In terms of Christianity and Judaism, both these religions had significant presence in the region. Not only Muhammad would've known of the deeply, most Arabs did. The Quran is full of lines like "you heard of (insert Old Testament prophet)" or "we know the bible says..."

At the time, oral traditions were the main way to spread information and history. So it's hard to find details outside of assumptions.