1) Goish music. Please define. Beethoven and Mozart were goyim, does your question apply to their music as well?
2) Woman singer. If you hold that recorded music is not the same as live (which is basis for listening to taped music during sefira and 3 weeks according to those who do), why should kol isha be any different?
3) Music during 3 weeks. May I refer you to Rav Simcha Bunim Cohens sefer on “the 3 weeks” where he has a lengthy discussion on listening to music. While he does state that many (most?) poskim dont allow listening to recorded music, there are some who permit it.
4) Again, Rav SB cohen discusses whether one must walk out of a room where music is playing (his example, a DRs office) and he writes you do not. Of course he writes this in the context of halachos of the 3 weeks, and in no way implies he allows someone to play non jewish music in the office, but, the listener likely does not have to walk out.