In an English work, can a non-English source be cited even if there exists an 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.
There are two issues here: what the ethical requirements are, and what will annoy readers.
Ethically, you have to make your citations clear and correct. If your information and page numbers come from the Romanian translation, then you need to indicate this explicitly. (The page numbers and even the details of the content could vary between translations.) As long as you do that, using the Romanian translation would be eccentric but not unethical.
On the other hand, it will almost certainly annoy your readers, given that you aren't writing for an audience you expect to have a special interest in the Romanian translation. You are making it much more painful for readers to learn anything from your citations, which can give a bad impression (like you don't care about your readers or don't expect anyone to ever want to look up these references).
Updating the references sounds like a pain, but it is worth doing if you can. If you can't do this before submitting your writing sample, then I would append a brief explanation/excuse. For example, you could explain that you wrote this paper for a Romanian audience and don't have the English translation available to update the references. This wouldn't give a great impression, but at least it makes it clear that you realize this is unusual and would fix it if you could.
If I correctly understand your question, you are including, in your writing sample, your own English translations of the Romanian translation of the original German book. As far as I know, that's fine, provided you make it clear that this is what you've done. For example, cite the original German book and its Romanian translation, and add that your translation is based on the latter.
Anonymous Mathematician said that this will make it much more painful for your readers to learn anything from your citations, and that's probably true, but I don't think the purpose of these citations is for the readers to learn anything. They will learn from your English translations. The purpose of the citations is to give proper credit to the author and the translator, and also to insulate you from blame if the Romanian translation that you used turns out to be inaccurate.