Aura will not re-issue lost tutorial items. Some tutorial missions are accompanied by tutorials which spawn items required by those missions. If a tutorial is skipped or disabled, that item will not be spawned.
Many missions require the fetching of an item, but are marked as completed when the item is dropped. I wonder if these completion triggers could be adjusted to be more like the new revision of "Cargo Delivery" where the trigger is the looting of an item.
Another suggestion about moving belts to grav sites. The interesting suggestion here is playing tutorial videos on CQ screen (e.g.: the probing tutorial).
Lowsec: some discussion about exploration, and a question about finding a region of lowsec in which to look for frigate fights.