You don't have to inform HMRC until you derive an income from the book, and even then there are exemptions available.
If you get a publishing deal, you may need an accountant........... but first write the book.

Misread date. Ignore second line.

It also begs the question of whether CGT was declared on the siblings' sale. If it was, then the value is established.
The OP's question is somewhat ambiguous. Was the property gifted by the father? If so IHT may be relevant.

"Under poor advice, he transferred a house into each of their names." Has he transferred a house to each daughter, has he transferred a half share in each house to both daughters, or has he only transferred one house to both of them? If so which one? If the former, he's lost the benefit of PPRR on h...

Yes, that makes sense.

Are the overpayments "material" or "insignificant"? That depends on the total gifted and is open to interpretation.
I wouldn't worry about it, as the chances of HMRC picking it up are very small.

My feeling is that until it's in your bank account, it's not income.

The limitation period for council tax is six years. It is set by regulation 34 Council Tax (Administration and Enforcement) Regulations 1992 (the regulations). The regulations state that a local authority cannot apply for a liability order more than six years after the day the debt fell due. from:ht...

Yes, as long as she signs it.

Yes.