1) послушать - I'm listening to you. прослушать: a) I've heard this song. b) means to miss. They were chatting to each other, and therefore missed the key announcement 2) Я был в москве месяц = I spent a month in Msk я еду в москву на месяц = I'm going to Msk for a month. 3) Он выучил уроки и поэтому хорошо прочитал их на вечере. Thе sentence is strange, I would even say incorrect. It will make more sence if one says: Он выучил стихи и потому хорошо прочитал их на вечере. Вечер means a concert in this case, or a meeting, similar to a small presentation. Not the part of the day. So we use the same rules as below: Он выучил ... и потому хорошо прочитал их на концерте.

1) Прослушать и Послушать There are almost no difference, but "прослушать" rather means that action is complited. Example: "I listened this audio." "Я прослушал эту аудозапись" - (likely from start to finish) "Я послушал эту аудиозапись" - (maybe just listened the interval) 2) The first sentence means "I was to Moskow about a month", the second means "I'm going to travel to Moscow by a month". Then the first means that somebody already have been to Moskow, the second means that somebody haven't been yet. In russian we say "на месяц", "на день", "на пару часов" but it doesn't means we're gonna on a month:D It means "by a month", "by a day", "by two hours". 3) "Он выучил уроки и поэтому хорошо прочитал их на вечере". In this case "вечер" doesn't means "tonight" or "evening". In this case it means sone event, where he readed a speech. More simply "вечер" in this case means some event, celebration etc. In russian you can use "вечер" if the evening will be some event and you can called this event "вечер". BTW, there are a word "Утренник" in russian. It doesn't means a morning. It means that sone event will be at the morning:D It's hard to understand, but I hope that you'll get it.