This is the first time we've seen Einige and the translations shown only include some form of Unite or Agree. How are we supposed to know it also means Some or A Few?
I always use a decent German -> English dictionary alongside Duolingo because, while it's getting better, it's not yet perfect. If you haven't seen a word before, take a few minutes to do a little research on your own accord outside of the site. This will also aid your memory of the word and register it more permenantly in your mind.
If I'm not at home or don't have a dictionary to hand, this is my best friend: http://dictionary.reverso.net/german-english/
Why not "Children like some people?" I'm confused about word order here.
In German grammar, the only thing that matters in word order is that the verb has to be in second position. This is a good example "Mit freunden spleile ich am Computer" (I play on the computer with friends)
Cases and conjugations. Ich spiele = I play, if the subject were "freunden," then spielen would be conjugated to third person plural, or "spielen." The word order is so flexible in part due to all the cases in German: the different articles allow for explicit identification of the subject, object, etc.
Not a German native, but: when you have such a simple sentence with a single subject, a verb and an object, the word order becomes important with the subject at the beginning, otherwise with no articles it becomes ambiguous (as you have pointed out).