DL is telling me that I need the article "a" with director. Not just any article, but "the article a." This isn't right is it? In English you don't always need the article here. Depends on context. I.e., she just got promoted. Now she's Director. She's not just "a" director; she's "the" director. Her title is now "Director." So, she's Director. "Она стала режиссёром."
This only works in combination with whatever that position is related to. "She became director of ..." or "... became leader of..." is absolutely acceptable, but just saying "She became director", especially without context whose or which director, sounds a bit odd (it's totally acceptable in colloquial speech, everyone understands it but I think the goal of Duolingo should also be to teach how to correctly use expressions, especially to non-native speakers). Think of it as a bonus lesson while learning Russian :)
Because the subject noun "она" takes the nominative case. The object "режиссёр" takes the instrumental case "режиссёром." Both nouns in nominative can be confusing because Russian has flexible word order, meaning that the subject doesn't have to come first in the sentence like in English. For example, this exercise could be Режиссёром стала она. Or, Режиссёром она стала. If the object режиссёр is in the nominative case, it's confusing when it comes first in the sentence, because it appears to be the subject instead of the object. That's why it's incorrect grammar
According to Wiktionary, стать + [instrumental case] = "to become [instrumental case]".
стать appears to be a quite versatile verb https://en.wiktionary.org/wiki/%D1%81%D1%82%D0%B0%D1%82%D1%8C#Russian
Я написал "She has become a director", но это было отмечено как неправильно. Правильные ответы: "She has become a movie director." "She became a director."
И вот я не пойму, если "became", то можно просто "director", а если "has become", то обязательно "movie director"? Или это просто не добавлен вариант перевода?
Sounds totally logical, however I fail to notice the difference between /ʃ/, /ɕ/ and /sʲ/. I believe my own language is to blame for that. As in English, in Dutch we don't have a single character for "sh" (in Dutch it's usually written "sj"). But whenever an "s" is followed by a "j"-sound, they are pronounced like "sj", even if they belong to different syllables or even different words. And to make things worse, it's not even clear what sound it really is. Check for example https://ru.wikipedia.org/wiki/%D0%93%D0%BB%D1%83%D1%85%D0%BE%D0%B9_%D0%B0%D0%BB%D1%8C%D0%B2%D0%B5%D0%BE-%D0%BF%D0%B0%D0%BB%D0%B0%D1%82%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D0%B9_%D1%81%D0%B8%D0%B1%D0%B8%D0%BB%D1%8F%D0%BD%D1%82 : here the Dutch "sj" is said to be either [ʃ], [ɕ] or [sʲ]. I guess that's why it all kind of sounds the same to me.
In the IPA, putting aside Dutch and English for a moment, the "сь" sound, /sʲ/, is just a palatalized S. That's it. There is no English "sh," no Dutch "sj," or no /ʃ/, /ɕ/, or /ʂ/, sound in it whatsoever. I can understand how it can confuse because of Dutch, and in English there is no palatalized S sound at all - only regular S. Just think of "сь" as an S sound and Щ as a palatalized and longer-held English "sh" sound.
When I write "сь," it's because the Russian vowel "Ё" palatalizes the Russian consonant "С."
General statements use indefinite articles. It's more common to say that she became "a director" when talking about her profession. When talking about a specific movie, then she became "the director." But without context, the first is the more common one. We probably wouldn't say "became the director" anyway. We would normally say "she is the director" or "she was hired as the director" or "she got the job as director" or "she is going to direct."