For those of you who have studied Jewish history, what I'm wondering is if (and how) Ashkenazi, Sephardi and Mizrahi communities kept in contact.
For one example, how did Passover melodies sung at the Seder which were invented in middle ages Europe (Adir Hu, Echad Mi Yodeah) reached the other Jews. Did this only happen in Israel later?
The best answer I can give is yes and no.
For yes:
-Religious scholars always discussed things among each other, regardless of where they lived. Sometimes these discussions could literally take years because of the extreme distances involved, but rabbis and sages did communicate. We even see early instances of stereotyping, where some sephardi rabbis thought Ashkenazi rabbis weren't up to snuff when it came to some legal opinions.
-Traders and merchants were constantly moving across Europe, and often visited both Ashkenazi and sephardi communities. The Rahdinites were a huge Jewish trading network, and their routes passed through both Ashkenazi and sephardi lands. Apparently the Khazar Correspondence was delivered to Hasdai ibn Shaprut by way of an Ashkenazi middleman.
-After the expulsion from Spain, many sephardi moved to communities neighboring existing Ashkenazi populations. Holland was a very big destination, and it is right next to the Rhineland, which is where the Ashkenazi began. Northern Italy, especially around Venice, saw a lot of Ashkenazi and sephardi cohabitation. The northern Balkans also had the sephardi moving into places like Serbia and Bulgaria, where they may have had contact with Romanian and Hungarian Ashkenazi communities.
For no:
-The average Ashkenazi would probably have never have met a Sephardi, and vice-versa. Communities, both Jewish and Christian, were extremely isolated from each other. Just like a Pole living in Warsaw would probably never meet an Italian in the 15th century, an Ashkenazi Jew would probably never meet a sephardi.