Learn Croatian: Morate pažljivo čitati dokument. - You must read the document carefully.

It comes from the adjective pažljiv, which means 'careful'. To make it an adverb ('carefully'), we simply use the neuter singular form of the adjective, which adds an -o to the end. This is the standard way to turn regular adjectives into adverbs in Croatian.

Why is pažljivo placed before the verb čitati?

In English, we usually put the adverb at the end of the phrase ('read carefully'), but in Croatian, it is much more common and natural to place the adverb right before the verb it describes.

Why do we use the dictionary form čitati instead of conjugating it?

Because it follows the verb morate (you must). Just like in English, when you use a modal verb like 'must', 'can', or 'want', the main action verb that follows it stays in the infinitive (dictionary) form.

Since dokument is the direct object being read, why doesn't its ending change?

You are right to expect the accusative case here! Dokument is a masculine noun. For non-living (inanimate) masculine nouns, the accusative case looks exactly the same as the nominative (dictionary) form. If it were a living masculine noun, it would get an -a ending.