I would like to share a folder containinga list of individual items, e.g.a grocery list, and have someone else able see the list and be able to add and/or remove and/or edit items.
I don't believe you can share folders, but you can share individual notes.
The note has to be saved in iCloud. Use the collaboration mode to share the note. When you or the person you shared with makes changes, you will be able see it.