The grammatical meaning of assertion is "a positive statement, usually made without an attempt at furnishing evidence"
There are many statements made by management in the financial statements in the form of notes to accounts. These may be called assertions by the managemen
When you go through the notes to accounts of a financial statement, you will see that the management gives some statements regarding the accounting policies, significant disclosures and other details which would be useful for the user of the financial statement.
Let us say there is some extraordinary item included in Other income. A note to this would be put in the notes to accounts. Now as an auditor, one has to ensure that the note made in this regard are free of material misstatements. The auditor has to assess the risk of material misstatements in these assertions. He may have to review the way/methodology adopeted by the management in making these assertions.
There may be other assertions which may have significant impact on user's understanding of financial statements.
I could not understand the types of assertions mentined by you. May be these are not types of management assertions but are the assertions (statements made) by an auditor.
Like if an auditor says that the financial statements are free of material misstatements, it would imply that the assertions made by management are complete, accurate and free from material mis-statements.
Hope it is clear.