Is "nuachtáin" spelled correctly in this instance? If so why?
Yes, it is. The object of a progressive sentence is in the genitive.
Does the genitive form always look like the plural version of the noun?
No, it does not. Sometimes the genitive singular is the same as the nominative singular. It just depends on the declension class.
You lost me at "declension class". Where can I look that up?
Gramadach na Gaeilge is where I suggest everyone start.
The sinking of the Titanic, perhaps?
What is a “historical newspaper”?
Are you really trying to make sense of Duolingo’s sentences? ^^’
I refer you to my downvoted answer below. I was serious I can't think what else a historical newspaper can be. The Bayeaux Tapestry, maybe?