2. Avoid mobile bills. They are not officially accepted but are not as powerful as broadband / landline. BT broadband is good proof because it is a service provided to a specific address. I will give the same answer I gave to number 1 regarding the content of the correspondence.
4. I have used the Royal Mail redirect confirmation myself and have had no problems. Car rental / insurance letters are not great and should be avoided if possible, but are not necessarily ineligible.
This is mainly my opinion based on observation, but:
Strong evidence: Utility bills for physical services (water, gas / electricity, broadband or landline), municipal tax statements, bank statements or correspondence showing you have an account, official government correspondence (HMRC, DWP, DVLA, UKVI / Home Office, NHS or GP, etc.)
Weaker evidence: Letters regarding insurance, mobile statements / bills, credit card statements, letters from other government regulated entities but not actual government entities (such as registered charities, Royal Mail, National Trust)
Bad proof (do not use unless you have absolutely nothing else): Receipts, invoices, letters sent by utility companies but which do not indicate that you have an account, letters from unofficial sources