"I will try that dress on."
I would think that "件" could be used as a classifier here too, but "我會試試那件裙子。" is rejected.
I'd also think that "試一下" would be an acceptable alternative to "試試", but that answer ("我會試一下那條裙子。") is also rejected.
Yes it is. Dresses, skirts, fish, ships, bedsheets, streets, news... You have to "stretch" a little bit the usual Western concept of long, thin and narrow things. As for the news, it dates back to when Chinese people would communicate writing on scrolls