Learn Hardcore German: Das Kind ist neugierig auf das Geschenk.

Kind is a neuter noun in German, so its singular definite article is das. Here das Kind is the subject of the sentence, so it remains in the nominative case.

Why isn’t the adjective neugierig inflected (no ending)?

When an adjective stands as a predicate after a linking verb (like ist), it does not take the typical adjective endings. It stays in its base form to describe the subject (predicate adjective).

Why is neugierig followed by auf? Couldn’t I use über instead?

Different German adjectives govern different prepositions. neugierig always takes auf + accusative—neugierig über is not a valid combination.

Why is auf das Geschenk in the accusative case and not dative?

auf is a Wechselpräposition (two-way preposition). With spatial movement it takes accusative, with location it takes dative. But here it’s not about space—it’s a required complement of neugierig, and by rule that complement is accusative.

What is the function of auf das Geschenk in this sentence?

It’s a prepositional object (ein Präpositionalobjekt). The adjective neugierig needs it to complete its meaning (“curious about something”).

Can I contract auf das Geschenk to aufs Geschenk?

Yes. In spoken and written German auf das often contracts to aufs, so you can say:
Das Kind ist neugierig aufs Geschenk.

How can I replace auf das Geschenk with a pronoun?

Use the pronominal adverb darauf. For example:
Das Kind ist neugierig darauf.

Can I change the word order, for example starting with the prepositional phrase?

Yes. German allows you to front elements for emphasis. You can say:
Auf das Geschenk ist das Kind neugierig.
The finite verb ist still remains in the second position.