The standard remote connection mechanism for all products is supposed to be migrating to REST based - which, of course, Connection supports: http://docwiki.cisco.com/wiki/Cisco_Unity_Connection_Provisioning_Interface_(CUPI)_API
The client SDK is really just ODBC - yes, you can do that for Connection as well - although you're on your own for figuring that out for Linux - you'll need to download the client drivers from IBM directly (the Windows drivers are available here: http://www.ciscounitytools.com/Applications/CxN/InformixODBC/InformixODBC.html)
There are 4 DBs - you can explore them using CUDLI you noted above: http://www.ciscounitytools.com/Applications/CxN/CUDLI/CUDLI.html - the directory DB (UnityDirDb) is by far the most used. CUDLI allows you to explore all the tables, views and stored procedures as well as view the data dictionary for the version of Connection you're attached to - I get you're a Linux house but I trust a Windows box of some flavor is available somewhere - it can be very helpful, I use it all the time.
The connection string used to attached to Connection using Informix's ODBC connection looks like this: "Host=192.168.0.1;Server=ciscounity;Service=20532;User ID=<login name>; password=<password>;Database=UnityDirDb;DB_LOCALE=en_us.utf8;CLIENT_LOCALE=en_us.utf8;Protocol=onsoctcp"
You'll need to turn on the ODBC proxy service on Connection and install the client SDK from IBM - other than that you should be good to go.
