What is the ruling on taking up the position of director of a youth hostel, given the presence of singing and impermissible activities within it, and the threat of losing one's job upon refusal?

As long as your assigned task is limited to housing young men, you are not sinful for any unlawful acts some of them may commit in the accommodation. The sin of unlawful acts falls upon the doer, not upon you. You are obligated to denounce their actions if you are able, otherwise, there is no blame upon you.