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)?