The user I created cannot add or edit products, even though I ticked the Products > Inventory > Products checkboxes. How to solve that?
When setting Resource Access to custom, make sure that you've granted separate permissions to add, edit and delete products. You can find the corresponding checkboxes under System → Amasty Role Permissions:
As soon as you adjust the settings, the user will have the possibility to add new products and edit the existing products: