If you have already applied for a visa using your present address, you will need to let INZ know your new address. If you haven't already applied, then when you do, you will need to state in your covering letter that you lived at x address from this date to that date, and that is where you first section of evidence refers to, then you moved to y address, and there is more evidence relating to your new home.
You don't have to have been on long journeys together. If you have seen other people talking about that, it is just that they happen to have taken a trip, so they collected proof that they were both at that viewpoint, that hotel, on that plane, etc. - just different things to add to the mix. It's not obligatory.