I\'m looking for a way to set up (via SQL) a log table containing everything that had been done to my sqlite database (preferably in terms of the insert, create table etc. state
Though the following doesn't meet all your requirements, you may wish to see one way to do it. Mike Chirico's SQLite Tutorial has a section on Logging All Inserts, Updates, and Deletes that mimics the functionality of MySQL's binlog.
It relies on triggers that must match the schema for each table whose changes you wish to track. That is, if your table has a field called "a", then the logging table needs to keep track of "aOLD" and "aNEW". In this way, the trigger is able to record updates, inserts, and deletes made to the fields in that particular table.