How do you know its 'child' or 'children'?
Context. In this case, you can't have "child" so the noun has to be in definite or indefinite form. For singular, this would be "barnet" (definite) or "et barn" (indefinite).
Is the "does" always implied?
"Does" is something peculiar to English. Other languages don't use the word "does" like English... does.
Are "som" and "at" interchangable?
Not in any case that I can think of.
I though both of them mean "that" so what is the difference?
Indeed, they both can, but they're not the same "that":
Try asking the same question without the word "does". Now try saying the same thing as a statement.