What is the ruling on working for an economic news satellite channel that presents a program solely about cinema news, with the work restricted to archiving these programs, which contain unveiled female presenters and background music, and what is the ruling on the salary resulting from that?

Your work in storing programs that contain images of immodestly dressed women and music is a clear aid to forbidden acts, and Allah has forbidden cooperation in sin and aggression. If the channel agrees to store programs free of objectionable content, then all praise be to Allah. Otherwise, you must leave this work, unless you are compelled to remain in it, such that you cannot find what suffices your needs and the needs of those you support, and you cannot find another job. In that case, it is permissible to remain until the necessity is removed. Be certain that provisions are predetermined, and "whoever fears Allah – He will make for him a way out and will provide for him from where he does not expect."