What is your opinion about following: Can a non-native English speaker do proofreading as well (e.g. a translator)? Or do you think that he/she will never be able to spot mistakes and correct sound of English language?
I think they can do it, but their work quality depends on how proficient they are!
A good, diligent non-native proofreader will be better than a poor, sloppy native one. It depends on their level of fluency, their expertise in the area, etc, and many other factors.
I worked for a printing/publishing company in the 1970s, and they preferred non-native speakers for galley proofs. Apparently non-natives did not get distracted by 'reading' the texts; they were just great at spotting typos and physical printing mistakes.
However, the company always employed natives, usually experts in the field, on editing-proofreading.
A good and attentive non-native speaker will notice grammatical and spelling errors, even poor style and sentence structure, but one area that seems to be extremely difficult is the correct usage of a/the/nothing at all, especially the latter two (definite article or not).
Obviously there are rules and exceptions to the rules that one learns, but in my experience at least, even university professors of English like to have their writing, say, academic articles to be published internationally, double-checked for thes and lack thereof by a native speaker.