Do I have to send in products per country or does Amazon automatically distribute my goods across all marketplaces?

If you sell pan-European (PAN-EU) with SPACEGOATS, Amazon will take care of distributing your products all over Europe (if you have an active listing on each marketplace!).
If you want to send goods only to a specific country, your products will have to be delivered there directly with UPS. In this case, please state so clearly in the support ticket when creating a shipping plan.