Learn Croatian: Ministarstvo zdravlja je objavilo nova pravila. - The ministry of health has published new rules.

Enclitics usually go in the second position of a sentence. However, Ministarstvo zdravlja (Ministry of Health) functions as a single, cohesive noun phrase. While Croatian sometimes allows splitting a noun phrase with an enclitic, keeping it together is the standard, natural word order in modern Croatian.

Why does the verb end in -lo (objavilo) here?

The verb must agree in gender and number with the subject, Ministarstvo. Since nouns ending in -stvo are almost always neuter, the past participle takes the neuter singular ending -lo.

Could you use an adjective here, like zdravstveno ministarstvo, instead of the genitive zdravlja?

Yes, Croatian often prefers transforming a modifying noun into a relational adjective. However, for official names of government and administrative institutions, using the noun in the genitive case is the standard naming convention, making Ministarstvo zdravlja the proper official title.

What case is nova pravila in this sentence?

It is in the accusative case because it is the direct object of the verb objavilo (the things being published). It might look like the subject at first glance because for all neuter nouns in the plural, the accusative form is completely identical to the nominative form.