Does Azure SQL Data Sync support MySQL or SQLExpress? I did see that it supports SQL Server (2005 and later) but does it support syncing between a SQLExpress server or MySQL server and an Azure Server?

I'm trying to use it with a SQLExpress server but it isn't connecting. Is this because it's not supported?

The error I'm getting when trying to connect with SQL Data Sync 2.0 on my server computer is: Unable to connect to the Database. Please check if service account has connectivity, credentials, and permissions to connect.

I've opened up port 1433 in the firewall and can connect to the server via SSMS. However, the SQL Data Sync 2.0 application won't connect.

I'll be trying this with a MySQL server later as well so I just wanted to know if it's supported or not as well.
Azure SQL Data Sync does not support MySQL for synchronization but it does support SQL Server Express as you can read here. 

One of the troubleshooting steps is to exit local sync agent, then open the services.msc applet in Control Panel, make sure SQL Data Sync service is started, if the service is started please restart the service. If the service cannot start change the service account to a local Administrator of the computer. Reopen the local sync agent.

Try also to disable any security software (Avast, Windows Firewall). Start SQL Server Browser Service on the computer.

Another possible reason, the agent key that you have entered is invalid. The agent key being submitted is not the most recent; you may have regenerated a newer key on Azure Sync portal. Try regenerating on Azure portal and resubmitting.