"The children are from different cities."
Translation:De kinderen komen uit verschillende steden.
'Komen uit' is used to indicate where you are from in the meaning of where you live.
'Ik kom uit Nederland, ik woon daar' - 'I'm from the Netherlands, I live there'.
'Komen vanuit' is used to indicate the origin from where a movement is taking place.
'Ik ga naar Spanje en kom vanuit Nederland' - 'I'm going to Spain and I'm coming from the Netherlands'.
Using 'vanuit' in the sentence of this course, 'De kinderen komen vanuit verschillende steden', it would change the meaning to 'The children are coming from different cities'.
Hope that helps!
There is no such exercise. Within the Duolingo tree that's also not possible, because it would be way to long and boring only to focus on the gender of all nouns that are in the course. There is no fun way in saying this, but you simply have to learn the gender of every noun. There are a few rules (see here) and if you don't know "de" will be correct 75% of the time, but mostly you'll have to learn. If you're into drilling then you might find some tool outside Duolingo (e.g. Memrise).