If I add or delete an item on my next shipment, will it be added (or deleted) on all subsequent orders?

Yes. When you click the "Edit Products" button for a particular program, you can choose to make changes to all orders for that program, or for just your next order.

If you select "My entire Auto-Ship", the change you make to quantities of current items on the program or add new products will be reflected on all orders. 

If you select "My next shipment", the changes or additions you make will only affect your next shipment.  All other orders will remain the same.

The only exception to this is if you add a one-time product to your program, such as a toy - this will only be added once to your next order.  Don't worry, any one-time items will be clearly designated as such when you review your changes!