Severe mental problems

Yes, your mental health problems and insomnia count, however there's no guarantee that you'll get PIP. Send them docs letters, etc., but you have to make certain that you describe how you function for each of the questions. Just saying that you have these diagnoses won't get you anything. So, for example, for preparing and cooking a meal, do your mental health problems and insomnia make it difficult for you to prepare fresh food and cook it above waist height? Do you have to use an aid or appliance? Can you not do it at all? Why not? If you're on meds, do they affect your ability to cook? Explain that kind of thing for each question, and tell them about a time when your conditions caused a problem.

Filling out the forms is far more complicated than it looks - there are all kinds of rules and ways you should phrase things - not lie about it or anything, but they look for certain language. I'd ask CAB, Welfare Rights, or perhaps your CPN (if she knows how the process works) for help to fill them out.