Insurance: I'm with a specialist broker i4me.
Business rates: if your cottage is let on a commercial basis (definition available on business rates website - it differs slightly versus the HMRC definition for tax purposes) then you "have" to switch to business rates as it's a commercial enterprise. However, many people don't (for reasons below)....
Business rates are a lot more expensive than council tax but providing this is your only commercial property, you'll get 100% rebate meaning you pay zero. Which is fab.
However, as a commercial business, you "can't" use the domestic bin collection so have to pay a licensed refuse collector to take your rubbish (or get a license yourself, which isnt practical if you are a distant owner) and that frequently costs more than the council tax you would be liable for, hence people sometimes stay with council tax.
But some councils don't link up their business rates department with the refuse collection department, so when you switch, they don't take your domestic bins away and the refuse continues to be collected along with your neighbours.
It tends to be the tourist areas (Cornwall etc) that are hot both on the need to register for business rates, and when you do, remove domestic bins such that you will need to pay for a private company to take your refuse. Other less touristy councils are less likely to notice/care if you remain on council tax, and are less likely to notice/care if you switch to business rates so you may continue getting a domestic collection.
But bottom line is to be doing everything by the book, you should switch to business rates, get 100% rebate and pay for a commercial refuse collection.