VERSION
select banner from v$version;
COMPONENT INSTALLED
select COMP_NAME,COMP_ID from dba_registry;
CHARACTERSET
select * from nls_database_parameters where parameter='NLS_CHARACTERSET';
TRACE LOCATIONS
select * from v$parameter where value like '%/%;
TIMEZONE
select dbtimezone from dual;
DIRECTORIES
select directory_path from dba_directories;
This is the view could tell you most of about database operating characteristics...
NLS_DATABASE_PARAMETERS