Pension credit savings query, council tax reduction query please

Hi there, I wonder if anyone can help me get clued up ahead of time please.

A family member is in receipt of a State Pension + Pension Credit + Attendance Allowance (the higher of the two AA rate entitlements).

Her capital /savings have always been below £10,000 but her outgoings are seemingly less recently, so she could potentially start having savings + captial reaching above £10,000 which I understand would then need to be regularly reported to Pension Credit. I think.

I've a couple of queries please, if she were to save a good amount of money in future years.

1.) When a person declares to pension credit that they've savings of £10,500 for example. Does that trigger a review where they must request some bank statements all the way back to the beginning of the claim please? or is there no need to gather lots of paperwork and the sum is accepted? I'd love to prepare her for gathering this information if it's always necessary. Because it sounds like a temporary headache to me. But one that may well be necessary.

2.) If someone's pension credit is slightly lessened each week for them having savings above £10,000, at what point, if at all, does this affect council tax reduction please if at all?

-I'm not sure if i need to supply much more helpful information in order for anyone to advise me on that. (perhaps it's something I could contact uttlesford council about instead for their input)

Thank you kindly for anyone's time today.