When I asked my wife (a university trained fluent German speaker who lived several years in Berlin) about 'aussagen' she said she has never used it. She has been puzzled about the point of a number of words Duolingo has tossed my way. Her advice to me was to be a bit selective and not waste my time on words of marginal usefulness. Ironically, having now spent time finding out how useless a word aussagen is, I probably won't forget it.
My expectations are to be able to communicate in simple sentences while travelling and visiting with older, distant relatives in Germany. Some of the words Duolingo presents to me are quite useless in those situations... quartal or aussagen for example.
I have come to realize that there are thousands of people using this app, each with their own reasons to learn German. Duolingo is trying to be useful to people with a wide range of reasons for learning German, such as employment, university studies, immigration, etc. They are even getting us ready to watch a legal drama on television without having to ask what aussagen means.
I believe they are doing a marvellous job, especially considering the price.
I don't think so. http://en.pons.com/translate/german-english/aussagen
"speak out" would be "aussprechen" http://en.pons.com/translate/english-german/speak+out
It has more than one meaning: http://dictionary.reverso.net/german-english/aussprechen
No, http://dictionary.reverso.net/german-english/aussagen You would have to say "declare under oath" to mean "testify".
Don't forget that in English we can word things that way. In German you would perhaps use a form like "I do not promise you that I will do it." and "I promise you that I will not do it." " Ich verspreche dir nicht, dass ich es tun werde. " and "Ich verspreche dir, dass ich es nicht tun werde."