Some advise: Do it easy and logic.

1 tile = 1 unit (Be very carefull with using custom UOM.  Stick to ISO UOM, so you are sure not to get in trouble and misunderstandings).  You will the invoice no of tiles. And cost will by one tile. 

If you NEVER split a box, you might define in the description of a product that it is a box. Then one box = 1 unit.  You will then never manage individual tiles in you business.

Tiles are packed in Boxes.   Assume you only sell full boxes then use box as Product Package. Product package is used for sales.  You migt also define full pallet as product package for sale.  You can have price list for packages. 

But also define Box and pallets as Delivery Package.   Delivery packages can be moved around in warehouse, be related to a storage category than can have strategy for placement and qty defined by product, and shipped full or split.  (I am not sure that in Odoo you can assign boxes on to pallets).

Lot number are for traceability.  If you need traceability back to lot numbers (batches) of raw materials, use lot numbers. Else, avoid it. Delivery packages have unique numbers and will also give you traceability back to manufacturing orders.

Hope this helps you in decissions.