Try to just not answer yes or no to any assessor. If you do, make sure you follow on with an explanation. I.e. if asked if you can cook a simple meal? Don't just answer "yes" explain if you have difficulties doing it and how it affects you when you do. Just a simple example I know, but when asked any question, where the descriptors are relevant, always follow up with the what happens and why.
For the MR you should put this in writing stating where you think you should have scored those points and your reasons why. Then add a couple of real life examples of what happened the last time you attempted that activity for each descriptor that applies to you.You should avoid mentioning any lies/contradictions that may have been told in the report because they won't be interested in any of those. This link may help you. https://www.advicenow.org.uk/guides/how-win-pip-appeal
Slight variation on the yes/no answer....When asked if you can do something - and you can but maybe only slowly or with some other difficulty - I would answer 'No' rather than 'Yes but ...'The assessor will then need to either put 'No' - or ask further questions to clarify your answer.(I'm not suggesting anything dishonest - obviously if you can do something without any issues then the answer should be 'Yes')
I honestly have no idea how I can do it without mentioning those things. I'd just look like I was contradicting /lying about all the descriptors I've lost points on because of what the assessor has said that I've stated for them. Some of it doesn't even make sense.