"She is looking for the shopping cart."
Translation:Sie sucht den Einkaufswagen.
Is the "fur" in there superfluous to the point of being wrong?
für would indicate that the searching was done on behalf of, instead of, or for the benefit of the shopping cart (as in "I'll do the ironing for you = on your behalf, instead of you").
(And note that the correct spelling is für with an umlaut -- if you can't write that, write fuer instead of leaving off the dots.)
If German does use a preposition in connection with suchen, it's nach: Sie sucht nach dem Einkaufswagen.
I'm not sure how to explain the difference between Sie sucht den Einkaufswagen and Sie sucht nach dem Einkaufswagen except to say that the latter seems a bit vaguer or aimless to me.
I tried this: Sie sieht fur dem Einkaufswagen aus Why isn't that also correct?
- fur is not a German word. "for" is für with ü -- or fuer if you can't type ü
- für requires the accusative case, so für dem with dative dem is impossible
- aussehen is "look" as in "have a certain appearance" (sie sieht traurig aus = she looks sad), not as in "look for = search for"
Is "Sie sucht nach den Einkaufswagen" incorrect?
Yes, it is. That would be plural dative, but the English sentence only talks about one shopping cart.
Sie sucht den Einkaufswagen and Sie sucht nach dem Einkaufswagen would be possible in the singular -- note masculine accusative when den Einkaufswagen is the direct object but masculine dative after the preposition nach which requires the dative case.