Does anyone use modules in DB2 LUW?
I won't be able to answer all your questions, but for what it's worth:


SQL modules seem to be a part of the SQL/PSM 2008 standard. At least they appear in the draft version, that can be found on the interwebs.
Tools will eventually catch up with the server features. Meanwhile, you can use the Oracle-compatible PL/SQL dialect, currently supported by tools, to create PL/SQL packages, which are essentially the same thing.
Yes, people do use module. Many of the DB2 system-provided routines are implemented in modules.
While you can restrict direct invocation of routines outside modules by granting appropriate privileges, you cannot "modularize" anything without "modules".