Learn Hardcore German: Ich kaufe Vanille im Supermarkt.

Because Vanille is treated here as a mass noun (an uncountable substance). In German, when you speak about something in general (like “vanilla” as a flavor or ingredient) you often drop the article. If you meant a specific item (for example a pod), you could say die Vanille or eine Vanilleschote.

What case is Vanille in, and how can I tell?

Vanille is the direct object of the verb kaufen, so it’s in the accusative case. Since it’s a feminine noun without an article here, its form stays Vanille (unchanged). If there were an article, you’d see die Vanille in nominative but die Vanille in accusative as well (feminine – same form).

Why is im used before Supermarkt, and what does it stand for?

Im is simply the contraction of in dem.

in is a two-way preposition that governs dative here because it indicates location (“where” you buy).
dem is the dative masculine/neuter definite article.
Put together, in dem Supermarkt → im Supermarkt = “in the supermarket.”

When does in take the dative (as in im) versus the accusative (e.g. in den)?

With two-way prepositions like in, you use:

Dative to express location (answering wo?, “where?”): Ich bin im Haus.
Accusative to express movement or direction (answering wohin?, “where to?”): Ich gehe in das / in den Supermarkt.
In Ich kaufe Vanille im Supermarkt, you’re located inside the store, so it’s dative.

Could I use einkaufen instead of kaufen here? How would the sentence change?

Yes. einkaufen is the separable‐prefix verb meaning “to shop” or “to buy (supplies).”

Standard kaufen: Ich kaufe Vanille im Supermarkt.
With einkaufen you’d say: Ich kaufe im Supermarkt Vanille ein.
Note that the prefix ein detaches and moves to the end in main clauses.

Can I swap the order to Ich kaufe im Supermarkt Vanille? Is that also correct?

Absolutely. German allows you to reorder sentence elements for emphasis or style, as long as the verb stays in second position.

Ich kaufe Vanille im Supermarkt. (focus on Vanille)
Ich kaufe im Supermarkt Vanille. (focus on location)
Both are grammatically correct.

Why is ich lowercase while Vanille and Supermarkt are uppercase?

In German orthography, all nouns are capitalized, so Vanille and Supermarkt get an initial capital. Pronouns like ich, however, are not capitalized (except at the beginning of a sentence), unlike English where I is always uppercase.