No. It describes the outcome of the particular search or response. It does not establish that an event never occurred.
It can. Provide documented spelling variants or corrected identifiers and explain their relevance, without assuming every system searches the same way.
No. A schedule alone does not establish the actual disposition of a specific file. Seek a documented transfer or disposition where available.
That depends on whether you are challenging a determination or changing the scope. Follow the applicable instructions and do not assume a new request preserves appeal rights.
Name the responding office, scope, date, and actual wording. Avoid claiming that no record exists in any other repository.