Hi matiasbenedetto!
Thanks for your note. Meanwhile the problem is solved. For some pages there were pre-produced entries in the post excerpt fields in the posts table of the database. Probably from the template and still stored even after I had reworked existing page templates.
However, after the reworking, the contents of the post excerpt fields did not renew. And so, the English stuff came to light from the templated in the search results.
I deleted all post excerpt content with demo content in the database and now it finally is running.
Maybe this solution is helpful for others who face the same problem.
Alle the best!