1. Do bills or letters for Home Insurance or Private Health Insurance count as items of correspondence? They are delivered to us via the post.
Yes, they should be okay to use.
2. We have a joint account with one bank, and I have my own account with another bank. Does this count as one source or two?
One source.. because they both come from a bank/financial institution.
3. Our bank statement covers from the 10th of one month to the 9th of the following month. If we want to provide an item of correspondence for a certain month, I'm thinking we should use the statement that ends in that month. Is that correct? Or could we use either one?
It will only count for the end date on the statement... because you won't have received that statement until after the 9th of the following month.
i.e. for the statement May 10th to June 9th, it won't have been mailed to you until after June 9th, so you can only use it for the month of June.. you cannot claim that you received it in the post in May, because that would have been impossible.