Learn Russian: В чьей статье ты читал о происхождении этой редкой статуэтки? - In whose article did you read about the origin of this rare statuette?

It is in the prepositional case to match the feminine noun статье (article). The preposition в (in) triggers the prepositional case here to indicate location. Notice that for feminine nouns, the pronoun чья (whose) conveniently takes the form чьей in the genitive, dative, instrumental, and prepositional cases.

Why does the word происхождении end in -ии rather than the usual prepositional -е ending?

The dictionary form is происхождение (origin), which is a neuter noun ending in -ие. Nouns ending in -ия or -ие have a special rule: they take -ии in the prepositional case instead of the standard -е.

What case is этой редкой статуэтки in, and why?

It is in the genitive case. While the preposition о (about) puts 'origin' into the prepositional case, the rest of the phrase expresses 'of this rare statuette.' In Russian, the 'of' relationship is shown by using the genitive case for the following nouns and adjectives.

Why does the genitive form of статуэтка end in -и instead of the regular feminine genitive -ы?