Learn Hardcore Ukrainian: Я купив два яблука в магазині.

The nominative singular of “apple” is яблуко.
Its genitive singular is яблука, hence два яблука.
If the number were 1, you’d use одне яблуко (nominative singular).
If it were 5 or more, you’d use the genitive plural: п’ять яблук.

Which case is магазині in, and why?

магазині is the locative (also called prepositional) case of магазин (“store”). Ukrainian uses the locative with prepositions like в/у or на to indicate a static location (“where”). So в магазині means “in the store.”

Why is the preposition в used here instead of у?

Both в and у mean “in/into,” but they alternate to smooth pronunciation:

Use в before words starting with a vowel or a single consonant cluster that sounds natural: в магазині, в офісі.
Use у before words beginning with certain consonant clusters that would be awkward with в: у Львові, у Франції.
In everyday speech в магазині is standard.

How would I say “I went to the store” (i.e., motion toward the store)?

When expressing motion into/onto a place, Ukrainian uses в/у + accusative case. For an inanimate masculine noun like магазин, the accusative form is identical to the nominative:
Я йшов в магазин.
(“I was going to the store.”)

Why is the verb купив used instead of купила or купило?

In the past tense, Ukrainian verbs agree with the subject’s gender and number:

купив – masculine singular
купила – feminine singular
купило – neuter singular
купили – plural
A male speaker says Я купив, a female speaker says Я купила.

Why are there no words for “a” or “the” in Я купив два яблука в магазині?

Ukrainian has no articles (no equivalents of “a,” “an,” or “the”). Definiteness or indefiniteness is understood from context, word order, or additional words like цей (“this”) or якийсь (“some”).

Can I change the word order, for example В магазині я купив два яблука?

Yes. Ukrainian word order is relatively flexible and is used to shift emphasis:

Я купив два яблука в магазині. (neutral)
В магазині я купив два яблука. (emphasizes where)
Два яблука я купив в магазині. (emphasizes what/quantity)

Is два яблука here in the accusative case or the genitive case?

As the object of купив, the phrase два яблука functions as an accusative object.
Internally, however, the noun яблука is in the genitive singular because the numeral два triggers genitive singular form.

Where does the stress fall in магазині and яблука?

магазині – stress on the last syllable: мага-зи-нÍ (в магазина́х for plural).
яблука – stress on the first syllable: Я́блука.

Why do we say в магазині (“in the store”) but на ринку (“at the market”)?

Prepositions в/у are used for enclosed or indoor spaces (buildings, rooms): в магазині, в офісі, у кімнаті.
Preposition на is used for open spaces, elevations, events, or activities: на ринку (“at the market”), на пляжі, на уроці.