Re: Car Taxing.
You can't tax a vehicle more than a couple of weeks early otherwise you lose the months in between, i.e. if your tax runs out on July 31st, you can't tax it before about July 15th otherwise you'll end up taxing it from July 1st. I'd wait for the letter to come through because it will have a 12 or 16 digit long number on it that will make your life a whole lot easier.
Make sure you're going through the gov.uk website and not one of the rip-off sites. As for renewing your driving licence, you can do this over the phone if its just to change your address.