"Are you signing it?"
Translation:Skriver du under det?
Not a native Norwegian, but having lived in Norway for 30+ years, I'm kind of missing "på" in that sentence (Skriver du under på det) - otherwise it almost sounds like I am physically writing beneath something. Alternatively, drop the "det" at the end and just ask someone: Skriver du under?
Underskrive and skrive under (and undertegne) means exactly the same, whether to use compound or not is a question of style and form. As you can see the uncompounded version gets split by the object in a question, you could say Underskriver du det? but personally I would prefer the original (I can't really tell you why, maybe it's my dialect)
The signature itself is always called underskrift (m).
Undertegne also gets used as an adjective (in past participle, undertegnede) when referring to the signee of a document, a legalese way to avoid saying "I" (Jeg), or also when obviously referring to yourself when telling a joke.
I had to google this, but as far as I understand it's not exactly like in German. In Norwegian you will have a choice to split some words, but my source says that in German separable verbs are compounded in the infinite, but has to be separated in present and preteritum (I am doing the German tree so I guess I just learned something useful).
Du hast etwas sehr nützlich gelernt. And quite complicated too. This is one of the worst things about German. I am almost at the end of the German Tree and I am yet to come across a skill addressing the separable verbs. You'll have to study them on other places on the internet.
And thank you for your answer.