I don't fully agree with all the definitions - eg I think methods are not really philosophical approaches (although they arise partly from them) - they relate to the sorts of evidence we gather and how we go about it. Tools are the documents we use for assessment - incl criteria for marking, instructions etc.
I'd like to see a distinction between written and other (eg practical) methods as well as between subjective and objective assessments (eg online multiple choice which is very useful esp for formative assessment and assessment of recall and comprehension).
'Supporting...' - I don't think we should talk about 'multiple choice questions for summative assessment' unless we talk about their limitations in terms of Bloom's taxonomy. You touch on this in the prev paragraph but I think it needs to be a bit stronger.
For #6 (demonstrating knowledge and understanding) essays are often not the best method - objective assessment is often better for learners and teachers.
I think it'd be good to have examples of tools for different methods - eg instructions and marking criteria for a practical assessment, multiple choice (Moodle?), rubric for achievement-based assessment.