I need to find when and which user created full text catalog, and who added/modified/deleted the columns (that were full text indexed) in that full text catalog.
You have to use DDL event groups that can be used to run a DDL trigger or an event notification, and also the Transact-SQL statements they cover.
Refer BOL for more details on what can be tracked.
I have posted an answer here for How to get notified when a deadlock occurs using Event notification. The concept is similar and can be applied to audit Full text catalog.