Basically you are right about the third person-s. But this construction here is subjunctive, which means that there is no s. In German that would sound like this: "Ich wünsche, dass sie mir das Frühstück bringe". We do not use this form a lot in mundane language but it is being used in English speeches or in written language.
I think that I have to start again a course of English.... sometimes the third person singular gets an "s", sometimes not in these subjunctive exercises. Can someone explain me why? (btw, I translated this sentence as followed: I want that she brings me breakfast. It was corrected: I want that she bring me breakfast). Thanks!
The correct subjunctive is "I want that she bring me breakfast" (not "brings"). This would be considered incredibly awkward in normal spoken English, however. You would say "I want her to bring..." or "I want for her to bring..." To sum up:
She brings me breakfast. (not subjunctive)
I want that she bring me breakfast. (subjunctive: correct, but not common)
I want [for] her to bring me breakfast. (the most natural translation)
I am a professional writer and my English grammar is, in general, impeccable. I wrote "I want that she brings me breakfast." I can't explain why. I just know that that's how I would say it. This is a very fine point in English and I don't think most native speakers would recognize the difference.