The "v" in "doivent" is audible, so you have to infer that it is third person plural. With third person singular, you would either hear no consonant at the end of "doit", or you would hear the "t" (if "doit" was followed by a vowel). A lot of times you have to listen for liaisons in order to determine the meaning correctly. http://french.about.com/library/pronunciation/bl-liaisons.htm
It has now. Duolingo does not always first present us with hints to the meaning of the words, or the correct choice of meaning, but gives us different kind of exercices and expects us to make our best try, reflect upon the result, ask each other, books or other resources for explanations and then repeat the unit until we master it.