Learn Hardcore German: Im Schlafzimmer steht ein großer Schrank.

Because im is simply the contracted form of in dem, which you use whenever in (a preposition) combines with dem (the dative masculine or neuter article).

What case does Schlafzimmer take, and how do we know?

It’s in the dative case. In German, in takes the dative when it indicates location (i.e. answers “where?”), so in dem Schlafzimmer becomes im Schlafzimmer.

Why do we use steht instead of ist?

German often uses position verbs (stehen, liegen, sitzen, hängen) to describe where things are. Stehen is used for upright objects (like a wardrobe), while ist just means “is” and doesn’t specify position.

How do I decide between stehen, liegen, sitzen, and hängen?

Choose based on how the object naturally rests:

stehen for things standing upright (cupboards, lamps)
liegen for flat items lying down (books, papers)
sitzen for things/people “sitting” (a cat on a chair)
hängen for things hanging (pictures, coats)

Why is it ein großer Schrank and not einen großen Schrank?

Because ein großer Schrank is the subject (nominative) of the sentence. If it were the direct object (accusative), you would say einen großen Schrank.

Why does groß take the ending -er here?

After the indefinite article ein in the masculine nominative, adjectives use the strong ending -er to signal gender and case: ein groß‑er Schrank.

Why is the verb steht in the second position and the subject ein großer Schrank after it?

German main clauses follow the “V2” rule: the finite verb must be the second element. Since you start with Im Schlafzimmer, steht comes next, and then the subject.

Can I start the sentence with Ein großer Schrank instead?

Yes. If you front the subject, it stays in second position for the verb:
Ein großer Schrank steht im Schlafzimmer.

How would I ask “Is there a big wardrobe in the bedroom?” in German?

Turn it into a yes/no question by placing the verb first:
Steht ein großer Schrank im Schlafzimmer?