To add to what Tracey’s told you, have a look at the points table. PIP is divided into Daily Living (like DLA for Care) and Mobility, to get the maximum award for each, the applicant need 12 points for each component. https://www.citizensadvice.org.uk/Global/Migrated_Documents/adviceguide/pip-9-table-of-activities-descriptors-and-points.pdf
You score the highest that applies for each Activity. So if a person can cook with assistance, they score 4 points for that Activity. Then whatever other points apply for each of the activities are added up.
The care plan from the Local Authority will be very useful to include as evidence. You can ask the occupational therapist to write a letter stating what equipment has been supplied and is in use still, even if the equipment was supplied a long time ago. You can also include photographs as part of your evidence. For example, I included a photo of my wet room, showing the shower chair and grab bars.
If you can get the CAB to help with the form then do, otherwise, if there’s any other local welfare rights services try getting help from them. There are also guides available from the CAB: Personal Independence Payment - Citizens Advice and there is also a website who provide members of their service with guides: https://www.benefitsandwork.co.uk/ but to access their guides you have to pay about £20.
Regardless of the way the application is made, gather as much evidence as you can, send photocopies, not originals and don’t miss the deadlines. If you think there’s a chance of missing a deadline, phone the DWP and see if you can get an extension as the CAB did for Tracey.
Before you post the completed application off, photocopy the whole thing, just in case.
Once the assessors have looked at the form and the evidence you’ve provided, they will decide if a physical assessment is needed or whether they can make a decision just from the paperwork, or maybe just with a phone call. If they need a physical assessment in their offices and it’s very difficult for the lady you care for to attend one, you can request a home visit. Sometimes they do this anyway (there are two companies involved in the assessments, one company does mostly home visits, the other does very few).
Hopefully it will all be OK and the lady will get the maximum entitlement easily without a physical assessment. I managed to go from a full, indefinite DLA award to a full PIP award with no physical assessment. The assessment should last for at least 10 years before I have to be reassessed.