Yes, you can include your formal diagnosis and the fact that you mentioned it at your assessment. You should say that you don't think the assessor has taken this into account, even though you mentioned the symptoms that were impacting your day-to-day activities in relation to the PIP criteria.
Yes, you can link it back to the evidence on the government website.
Ask as many questions as you need to.
BIS
Nothing on this board constitutes legal advice - always consult a professional about specific problems
For the criticism of the medical report, do I go into detail of every mistake or error the HP made or pick a few and mention this report is not reliable?
I can't tell you what to do here - because it has to be a personal choice. I would say, however, that your focus should be on the things that make a difference to the points that have been awarded. So, for instance, if the report is full of grammatical or spelling errors - that's not good, and you might mention it in a final paragraph - but it won't make a difference to the scoring - which is what you are fighting.
BIS
Nothing on this board constitutes legal advice - always consult a professional about specific problems