In an English work, can a non-English source be cited even if there exists an English translation? I'm not a native English speaker. I would like to cite a book originally written in German for a writing sample to be sent for admission purposes to a graduate school in the UK (MA programme).

There are at least two translations of said work: Romanian and English. I have read the Romanian translation, not the English one, because it was far more convenient to do so. Naturally I translated the Romanian passages to English and cited them appropriately, but the citations are based on the Romanian translation (e. g. I have cited a passage to be found on page 52 of the Romanian translation).

Is it a problem that instead of citing the English version of the book, I have cited and translated the Romanian version? I'm afraid so, because the reviewers probably don't speak Romanian, therefore they can't check whether the cited passage is REALLY there in the Romanian translation or I just made up the whole thing. Plus they might think I'm lazy.

If this is indeed a problem, I have to find all of these passages - which I have originally read in Romanian - in the English translation and rewrite all footnotes, bibliography etc. (e.g. the passage which is located on page 52 in the Romanian translation might be located in a different place, say page 63 in the English translation).
There are two things to address here. First, relax. The exact sources you are citing in a writing sample for an MA program are NOT what the admissions decision will be based on. It is unlikely anyone is going to check up on your citations and even if they do, they are not going to care.

The second thing is, it is generally best to use the original, untranslated source. When the original source is not in a language you are proficient in, using a translation is reasonable. If you are writing in English and need to use a translation, then using the English translation is best, unless there is a compelling reason not to. In the future, you may want to work with English translations, but again for a writing sample, no one is going to care.