"Barnet skærer sig."
Translation:The child cuts himself.
This is not referring to a child having psychological difficulties. It's more like "hey don't let the kid play with the scissors, he'll end up cutting himself".
But it's in the present tense, meaning he either is doing it now, or has done it in the past and (probably) will do it again.
Why "themselves" is not correct? From this phrase I cannot see if the child is a girl or a boy.
But you can tell that it's just one child.
So if you want to use singular "they", use the singular, "themself" -- "themselves" is plural.
(I'm not sure whether "themself" will be accepted by the course, though.)
According to this article https://en.oxforddictionaries.com/usage/themselves-or-themself the form "themselves" is correct to use here. Moreover, it is more appropriate in written context.
I agree with everything except your first statement. You can tell there is only one child. "Barnet" is Defined and singular. If it were plural it would have been "Børnene" or just "børn"
(I know my score isn't very high btw but I am danish so I would know lmao)
Definite singular article requires a singular reflexive pronoun. In this case "themself" is the correct genderless pronoun. English speakers very rarely use the genderless, though (especially singular). We usually wait for, or already have, more information about the gender.
You simply don't need it. Sig is enough. Selv is only added for emphasis. Of course there are certain times when it is required, but in this case it isn't.