HI
All the statements you mentioned are incorrect.
First one: it is prescriptive grammarians not descriptive ones that insist up on a conventional notion of correctness
Second One: the criterion of success is achieving communication and that means comprehensibility and intelligibility
Third One: the monitor approach does not increase fluency because it requires that students monitor their pronunciation, and that decreases fluency

The Lexical approach is an approach related to teaching vocabulary, you will find it in the lecture called Teaching Vocabulary, it is explained in full in there.
Regards