1.with words nobody around understands or listens,(both are possible;in former one: it's not understandable, maybe they spoke some, which could be other languages or not words they can get . In the meaning of second:probably they spoke too quietly so that nobody around got what they said ).. coolly,,invigoratingly >>in this context I see 시원하게 and 통쾌하게 are similar in meaning,시원하게 is rather close to invigoratingly;to refresh sb. Perhaps the whole sentence would be like this, Sb's spoken to sb or themselves too quietly or in a way nobody can understand around. Cause the speaker would've been teased or annoyed by sb/sth,so that he said sth in order that the listener around couldn't get what they were saying, and it made them feel refreshed..:P
2.내뱉다>>exhale>내뱉기(noun)exhaling 들이쉬다>>inhale