Learn Russian: Я прочитал недавно опубликованный файл.

It comes from the perfective verb опубликовать (to publish). For verbs ending in -ать or -овать, we take the stem (опубликова-) and add the suffix -нн- followed by standard adjective endings (-ый here). The double -нн- is the signature of full-form past passive participles.

Why does опубликованный have the ending -ый if it's the direct object? Shouldn't it be in the accusative case?

It is in the accusative case! Full-form participles decline exactly like adjectives. Because the noun it modifies, файл, is a masculine inanimate object, its accusative form looks identical to its nominative form. The participle simply matches this with the standard masculine inanimate accusative ending -ый.

Why is the adverb недавно placed before the participle?

Adverbs that modify a participle usually come right before it to form a single descriptive block (недавно опубликованный). This entire participial phrase is placed right before the noun it modifies (файл), which perfectly mirrors the English word order 'recently published file'.

Can I put the participial phrase after the noun instead?

Yes, you can. However, in Russian punctuation, if a participial phrase comes after the noun it describes, it must be separated by commas. So if you changed the word order, it would be: Я прочитал файл, недавно опубликованный.