Translation:Hij is ongerust over de toets.
Onrust and ongerust, is there a difference?
"Onrust(ig)" means restless. It's usually something you feel inside you.
"Ongerust" means worried. You are 'ongerust' about something, anxious, worried.
Onrust is a noun, restlessness. Ongerust stems from a past participle, as you might have guessed from the "ge" in it.
Zenuwachtig zou toch ook correct zijn in deze zin?
'Zenuwachtig' would be 'nervous', a bit different.
Is it posible to say "Hij is ongerust vanwege de toets"?
Yes that's possible!