Learn Hardcore German: Es kommt darauf an, ob die Sache eilig ist. - It depends on whether the matter is urgent.

In Es kommt darauf an, ob ..., Es is a “dummy” or placeholder subject (like English it in It depends on ...). It usually doesn’t refer to a specific noun; it just fills the subject position because German finite verbs normally need an explicit subject in main clauses.
So Es kommt darauf an = It depends (on it) / It depends.

What does darauf mean here, and why is it split from the verb?

darauf is a pronominal adverb: da- + auf. It stands for auf + something (i.e., on that / on it).
The expression auf etw. ankommen means to depend on something / to hinge on something. When the “something” is a clause (like ob ...), German often uses darauf to point forward to that clause.

It’s not really “split from the verb” in the separable-verb sense; rather, ankommen is the verb, and auf ... is the required prepositional element. In this idiom, that element is realized as darauf.

Why is it kommt ... an (split) instead of ankommt?

Because ankommen is a separable-prefix verb (an-kommen). In a main clause with a simple tense, the prefix an goes to the end:

Es kommt darauf an.

In subordinate clauses, it stays attached:

..., weil es darauf ankommt.

Why is there a comma before ob?

Because ob die Sache eilig ist is a subordinate clause, and German requires a comma before subordinate clauses. Here the ob-clause functions like the thing it “depends on,” so it’s set off with a comma:

Es kommt darauf an, ob ...

When do I use ob vs wenn? Could this be wenn die Sache eilig ist?

ob introduces an indirect yes/no question and means whether/if (in the sense of “whether”). It presents alternatives: urgent or not urgent.
wenn means if/when in a conditional or temporal sense.

With Es kommt darauf an, ob ..., you normally use ob, because it’s about whether something is the case:

It depends on whether the matter is urgent.

Using wenn would change the meaning toward a condition/time frame and would not fit the standard “depends whether” structure.

Why is the verb ist at the end of ob die Sache eilig ist?

Because ob introduces a subordinate clause, and in German subordinate clauses the conjugated verb goes at the end:

ob
- subject
  - (other elements) + finite verb
    So: ob die Sache eilig ist.

What case is die Sache in, and why?

die Sache is nominative because it is the subject of the subordinate clause ob die Sache eilig ist.
You can tell because it agrees with the verb ist (and because sein takes a nominative subject).

What does eilig mean grammatically here—adjective or adverb? Why isn’t it eilige?

Here eilig is an adjective used predicatively after sein: X ist eilig = X is urgent.
Predicative adjectives in German do not take endings, so it stays eilig, not eilige.

You’d see endings when the adjective comes before a noun:

eine eilige Sache = an urgent matter

Is die Sache literally “the thing”? What kind of word is it in German usage?

Literally it’s the matter / the affair / the thing, but idiomatically die Sache is very common for “the matter/issue” in a broad, everyday sense. It can refer to a task, topic, situation, or problem depending on context.

Can I omit darauf and just say Es kommt an, ob ...?

No, that would be ungrammatical in this meaning. The verb is auf etw. ankommen; the auf-part must be expressed. When what follows is a clause, German typically uses darauf:

Es kommt darauf an, ob ... (standard)

You can sometimes replace it with a full noun phrase:

Es kommt auf die Frage an, ob ...
But you can’t simply drop the auf ... element.

How would the word order change if I start with the ob-clause?

You can front the subordinate clause (less common stylistically, but possible). Then the main clause follows with inversion (verb-second rule):

Ob die Sache eilig ist, darauf kommt es an.
(= Whether it’s urgent—that’s what it depends on.)

You could also do:

Ob die Sache eilig ist, kommt darauf an.
…but that sounds incomplete because German expects es as the subject; the first version is more natural.

Is Es kommt darauf an always translated as “It depends”? Are there other common variants?

Yes, it most often corresponds to It depends. Common variants include:

Es kommt darauf an, ob/wie/wer/was ... = It depends on whether/how/who/what ...
Das kommt darauf an. = That depends.
Es kommt darauf an, worauf du Wert legst. = It depends on what you value / what matters to you.