Translation:Little Éva steps from the table to the bed.
We wouldn't use a definite article with a person's name in English. The little girl sounds fine, but the little Eva does not.
In one translation (in this group) I used "little" for "kis" and it was rejected (in favor of "small"). So for this one, I made sure translate it to "small" and it was rejected in favor of "little." The other sentence was something like "I step from the bed to the (kis) table."
Is there a legitimate reason for these to have different translations, or should I just report it?
You should report those instances. Just one word on this: it's much more common to say "little" when talking about children. "Small" sounds a bit derogatory for people; it's more used for objects and partly animals.
small Éva - height of the girl little Éva - age of the girl
In the Hungarian sentence are both English translations correct, because we don't know, if Éva is short, or young. Reported.