Learn English – “Is there any news” or “are there any news”?

As long as you are referring to more than one subject, I would go with:

There are not any employees in the department.

For referring to a single instance, I would go with "there is no"

There is no employee in the department.

If the topic has no plural form (or is rarely used with a plural form), then I would consider "there isn't any":

"There isn't any water" = There is no water

News is uncountable and is used with singular verbs. The -s is there because etymologically, it used to be a plural form. Etymonline says:

late 14c., plural of new (n.) "new thing," from new (adj.), q.v.; after Fr. nouvelles, used in Bible translations to render M.L. nova (neut. pl.) "news," lit. "new things." Sometimes still regarded as plural, 17c.-19c.

As to other nouns like this, I have looked through a number of Wiktionary and Wikipedia categories, and the closest I could come to similar examples is measles and billiards.

Yet another interesting (but not really similar) case is species. Wikipedia says:

Specie and species make a fascinating case. Both words come from a Latin word meaning "kind", but they do not form a singular-plural pair. In Latin, specie is the ablative singular form, while species is the nominative form, which happens to be the same in both singular and plural. In English, species behaves similarly—as a noun with identical singular and plural—while specie is treated as a mass noun, referring to money in the form of coins (the idea is of "[payment] in kind").