[Bug] SQLite inconsistencies with NULL

SQLite queries with javascript seems to handle strangely the NULL value.
INSERT INTO : put a correct NULL in the table
SELECT ... WHERE xxxx IS NOT NULL : does not select only NOT NULL rows, but all rows.
UPDATE xxx SET yyy = NULL WHERE zzz = 'aaa' : does not update with NULL but with 0.
I suppose it comes from the difficulties of max handling the NULL concept?
But I'm passing directly the string to sql_obj in javascript, so why should the database not update with NULL???