I have found the problem(s).
1. There was an unknown bug with the recent version, thanks to the FTP access I was able to find it and fix it as well. It was related to the category and taxonomy selectors – they were incorrectly processed in one of the cases, causing the english version to malfunction.
2. The index table was incomplete yet. If you change the index table configuration on the index table options page, you always have to click the “Create new index” button, so the index table re-generates with the new options.
Once you find the final configuration that suits you you don't need to do that again. If you add/change posts/pages/products they are automatically added to the index as well.
If you like my products, don't forget to rate them on codecanyon :)