When I get a question of this form on a quiz, noun と noun verb, does the order of the nouns I choose affect my score?
For example, it seems to me that “らーめんとすしがすきです” and “すしとらーめんがすきです” are both correct. If the English translation has the nouns in the reverse order, does the question get scored as an incorrect answer?
It’s common to see left-right inversions between Japanese and English. These generally have no effect on meaning.
As a rule, renshuu tries hard to not be capricious. Just answer the questions in the way that seems most natural to you, and use the in-quiz reporting to complain about anything that seems unreasonable.
The answers have nothing to do with the English (renshuu is not that advanced, heh.) - so if renshuu thinks that grammatically, the ordering you put in works, it'll let it go.