I discovered another problem with the products.
For the individual product, only part of it is translated and the icons are missing. The representation is correct in the standard language.
I have checked your first issue with icons and have found a problem.
I see you are using Pods which is not officially compatible and can have issues. I suggest reporting this to the plugin author as other users and inviting them to our GoGlobal compatibility program, we will be glad to help with compatibility.
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We suggest using compatible plugins as ACF or Toolset.
As for your case with icons, Pods are translated and you need to manually add the correct fields, settings and translate etc
Your German pod gebinde in English is a container, you need to edit this pods set it up in the same way and add the correct fields. Then edit manually your 2nd language taxonomy and add values to those fields. In 2nd language frontend template in 2nd language make sure you are using the correct 2nd language Pods/field.
We have a similar issue published here as a known issue: