Let's go by parts. I guess that here: I would like to adjust the stocks of the products so that each size also adjusts an inventory for the different warehouses the customer has. You are referring to our premium add-on ATUM Multi-Inventory. With this add-on you can create as many inventories as you want for a single product, understanding inventories as warehouses.
In any case, I leave you here the documentation of the add-on, where you will find useful info about how it works: https://forum.stockmanagementlabs.com/t/multi-inventory-documentation
And the link to the demo site in case you want to try the free trial and check if it suits your needs: https://www.stockmanagementlabs.com/addons/atum-multi-inventory/
In the other side, to do this ' is there a bulk action to set the warehouses for all for the products and sizes?' and to achieve what you say in the second point, we recommend to use our premium add-on ATUM Export Pro.
I also leave you here the documentation of the add-on: https://forum.stockmanagementlabs.com/t/atum-export-pro-documentation
And the link to the demo site: https://www.stockmanagementlabs.com/addons/atum-export-pro/
Hope that this helps, if you have any doubt after reading the docs and testing the add-ons, please let me know.