Ohne Leiter kommen wir nicht an die Lampe über dem Schrank.

Because German main clauses follow the verb-second rule: the finite verb must be in the second position.

Here, Ohne Leiter has been placed first for emphasis. Once that happens, kommen must come next, and the subject wir follows it:

• Ohne Leiter kommen wir nicht an die Lampe ...
• More neutral: Wir kommen ohne Leiter nicht an die Lampe ...

So the first position in German is not only for the subject; other parts of the sentence can go there too.

Yes, ohne eine Leiter is also correct.

German often omits the article when speaking in a general way about tools, materials, or means, especially in short, practical statements. So:

• ohne Leiter = without a ladder
• ohne eine Leiter = without a ladder / without any ladder

The version without the article sounds a bit more compact and idiomatic here. The version with eine is more explicit.

Ohne always takes the accusative.

So if you include the article, it would be:

• ohne eine Leiter

because Leiter is feminine, and the feminine accusative indefinite article is eine.

Here, an die Lampe kommen means to reach the lamp or to be able to get at the lamp.

This is not just the basic idea of kommen = to come. The combination an + something + kommen can mean physically reaching something.

So:

• Wir kommen an die Lampe = we can reach the lamp
• Wir kommen nicht an die Lampe = we can’t reach the lamp

English speakers often expect something like reach, but German commonly expresses that idea with an etwas kommen or colloquially an etwas rankommen.

Because an die Lampe kommen focuses on reaching the lamp physically.

• an die Lampe kommen = reach the lamp / get at the lamp
• zu der Lampe kommen = come to the lamp / get to where the lamp is

So zu would sound more like movement toward the lamp’s location, while an here gives the idea of being able to touch or access it.

Yes. In this sentence, die Lampe is accusative.

That is partly because the expression here is an etwas kommen, which uses an with the accusative in this meaning.

Also, Lampe is feminine, and the feminine singular definite article is:

• nominative: die
• accusative: die

So the form stays die, even though the case is accusative.

Because über is a two-way preposition. It can take either:

• dative for location (where?)
• accusative for movement toward a destination (where to?)

Here the lamp is simply located above the cupboard/cabinet, so this is a static location, and German uses the dative:

• über dem Schrank = above the cupboard

If you said über den Schrank, that would suggest movement to a position above the cupboard.

Because of über in a location meaning.

Schrank is masculine: der Schrank. In the dative singular, that becomes dem Schrank.

So:

• der Schrank = nominative
• dem Schrank = dative

Since the lamp is above the cupboard in a fixed position, the dative is required.

Here nicht comes before an die Lampe, giving:

• kommen wir nicht an die Lampe

This is the normal placement when nicht negates the idea of reaching the lamp.

In German, nicht is often placed before the part it negates, or before the final element of the verbal idea. Here the meaning is:

• we do not reach the lamp
• we can’t get to the lamp

So nicht appears before the phrase an die Lampe.

Schrank is a general word for a large storage piece of furniture, and depending on context it can mean:

• cupboard
• cabinet
• wardrobe

In this sentence, cupboard or cabinet is probably the best fit, but the exact English word depends on the situation.

Not always. German has two different words spelled the same way:

• die Leiter = ladder
• der Leiter = male leader / manager

In your sentence, only ladder makes sense. If there were an article, it would help show the difference:

• ohne die Leiter = without the ladder
• ohne den Leiter = without the male leader

Because there is no article here, context tells you which meaning is intended.