To Dark Night:
Chapter 3 will be standalone if you want it to be. The items acquired in the first and second chapters won't have any use in the third chapter, but you won't have your oil/tinderboxes/laudanum. So it's really up to you. My suggestion is this: Load the most recent save. It should have saved in the Atrum Andron, so all you have to do to keep your items will be to play through that one more time (which should be quick if you have already done it) and then through the shrine.
I say you should try to have all the items from the first two because there is a surprise ending which nobody (to my knowledge) has attempted before, and you'll need all the help you can get