Cycling is the same word than biking, no?
Yes, you can see that by hovering over the word.
The given translation seems odd to my UK ears. While not a literal translation from the Dutch, I would probably use the expression 'to ride a bike'. Of course, I might just be old-fashioned :-).
In American English is would be more common to say "Are the children riding?"
The children are biking?
Is also a possibility.
No, it's a question, the equivalent of your question would be "de kinderen zijn aan het fietsen?" Implying you wouldn't expect them to be biking right now.