excluding non english field values from search_api index (or facet)
I will venture a guess that when choosing indexed fields for the Product CT, you selected 'Factories' field and created the facet against this. Since you are using node translation, it is quite sensible that all available nodes (in various languages) are displayed in the facet. I suggest you try the following:


Remove/disable field 'Factories' from the list of indexed fields and remove the respective facet
At the bottom of the fields configuration for the index, you will find an option labeled 'Add related fields'. Choose field 'Factories'. With this action, all fields of the referenced Factory CT will become available for indexing
Enable the field that is correlated with the translation source node. Label should be something like this 'Factories >> Translation source node'. Create a new facet against this field
Clear indexed data and re-index


Most probably, the new facet will only display the facet terms in the default translation language (English in your case)