I have defined a security rule and assigned it to my responsibilty, but is still does not work, why?

Make sure that you have enabled security at both the segemnt and value set levels, it must be enabled at both these levels to work. Also make sure you have switched out and back into the responsibility. 

My security rules don't work for the Account Analysis and General Ledger reports in Release 11.0.3.

This functionality is available starting in Release 11i. In Releases 11 and lower, one cannot set security for standard reports. Security Rules will only limit users from a few functions (e.g. Account 

In Rel 11i with the intercompany segment being used, is it possible to have a security rule on the balancing segment (company) without it affecting the intercompany segment, since they share the same value set?

Yes it is possible. You would enable security on the value set, but then on the flexfield segment (intercompany) you would not enable security. 

You cannot apply different security rules to the same responsibility for different users based on the user ID. You will have to create a new responsibility and define its own security rules. Then you can 

Security rules apply only with regards to creation/modification of lines within a journal. They do not apply when the journal is posted. 

Flexfield Value Security gives you the capability to restrict the set of values a user can use during data entry. With easy-to-define security rules and responsibility level control, you can quickly set 

Can Security Rules prevent users in one organization in the same set of books from adding Cross Validation Rules to another organization?

There is not a way in the same set of books, to prevent users from one operating unit via security rules, from changing cross validation rules for another operating unit. The only way to do this would 

Every Country has a Global Manager or User Responsibility to access Global SOB but it is supposed to limit users to their own Legal Entities. However, an Argentian journal can be posted by the Chilian user. How is this possible? 

This is working as intended. Security rules will prohibit a responsibility from being able to enter in certain values as well as prohibit the viewing of those values as well. However security rules will 

Forgot to check the security enabled flag for each segment and it is not updatable. How do I correct this?

Check your Accounting Flexfield Structure possibly it is frozen. Unfreeze the Structure and then you should be able to enable Security for the Segment.    

In General Ledger,a security rule of a parent with children, was setup to include the parent and assigned to a responsibility however, it is not functioning properly.

System allows the account the customer wanted but doesn't disallow the ones that are children of the parent values excluded.