Learn Hardcore German: Brauchst du Hilfe mit dem Stoff, ruf mich heute Abend an. - If you need help with the material, call me this evening.

So the verb-first order (Brauchst du …?) makes it look like a question, but combined with the second clause it functions like an informal conditional: If you need help, then call me…

Could you also say Wenn du Hilfe brauchst, ruf mich heute Abend an? Is there a difference?

Yes, you absolutely can say that, and it is very common:

Wenn du Hilfe brauchst, ruf mich heute Abend an.

That is a straightforward conditional sentence: If you need help, call me this evening.

Difference:

Brauchst du Hilfe, … is slightly more colloquial and has a more spoken, sometimes more direct feel.
Wenn du Hilfe brauchst, … is neutral standard German and works in both spoken and written language.

In many everyday situations, they are interchangeable.

Why is there a comma between Brauchst du Hilfe mit dem Stoff and ruf mich heute Abend an?

German uses a comma to separate two main clauses, even when there is no conjunction like und or dann:

Brauchst du Hilfe mit dem Stoff,
ruf mich heute Abend an.

Formally, you could also write:

Brauchst du Hilfe mit dem Stoff, dann ruf mich heute Abend an.

In English we might use If you need help with the material, call me this evening.
In German, the comma marks the boundary between the “condition” clause and the “result” clause, even though both are grammatically main clauses.

Why is it ruf and not rufst or rufen?

ruf is the imperative form of anrufen for du:

du rufst an → Ruf an! (imperative, “Call!”)

Some patterns:

du machst → Mach!
du kommst → Komm!
du rufst an → Ruf an!

You only use rufst in statements/questions with du:

Du rufst mich heute Abend an.
Rufst du mich heute Abend an?

The imperative drops the -st ending and often the -e as well (rufe → ruf), especially in spoken German.

Why is it ruf mich an and not ruf an mich?

The verb is anrufen, a separable verb:

infinitive: anrufen
main clause: Ich rufe dich an. (verb splits: rufe … an)
imperative: Ruf mich an!

The prefix an goes to the end of the clause, and the object (mich) goes between the verb and the prefix.

ruf an mich is ungrammatical, because native speakers treat anrufen as a single unit that gets split into ruf … an, not ruf an …. The prefix cannot go before the object in this structure.

Why is it mich and not mir?

mich is the accusative form of ich (direct object), while mir is dative (indirect object):

ich → mich (accusative)
ich → mir (dative)

The verb anrufen takes a direct object in accusative:

jemanden anrufen = to call someone

So you must say:

Ruf mich an. – Call me. not
Ruf mir an. – incorrect in standard German.

(With some other verbs, you do use mir:
Hilf mir! – Help me! (dative))

What exactly does der Stoff mean here?

Stoff is a very flexible word. Its main meanings are:

fabric, cloth
- ein schöner Stoff – a nice fabric
(learning) material, subject matter
- der Lernstoff / der Unterrichtsstoff – the material you have to study
colloquial: drugs
- harter Stoff – hard drugs

In your sentence, Stoff clearly means learning material, like topics from a course, textbook content, exam material, etc.
So Hilfe mit dem Stoff ≈ help with the (course) material.

Why is it mit dem Stoff and not mit den Stoff or something else?

Stoff is masculine in German:

nominative singular: der Stoff
accusative singular: den Stoff
dative singular: dem Stoff

After mit, German always uses dative:

mit dem Stoff
mit dem Lehrer
mit der Lehrerin
mit den Schülern

So mit dem Stoff is correct because:

mit → requires dative
Stoff (masculine, singular) in dative → dem Stoff

Could you also say Hilfe beim Stoff or Hilfe bei dem Stoff? What’s the difference between mit and bei here?

Yes, you can also say:

Brauchst du Hilfe beim Stoff, … (spoken: beim = bei dem)

mit vs bei:

Hilfe mit dem Stoff
Emphasizes help handling/working through the material.
Hilfe beim Stoff
Very common colloquial phrase; sounds like help with the material (as a topic/subject you’re learning). Slightly more idiomatic in some regions.

Both are fine and natural. beim Stoff may feel a bit more idiomatic to many speakers in school/university contexts, but mit dem Stoff is also perfectly acceptable.

Why is the word order Ruf mich heute Abend an and not Ruf heute Abend mich an?

Normal, natural order here is:

verb (imperative): Ruf
pronoun object: mich
time: heute Abend
separable prefix: an

→ Ruf mich heute Abend an.

Rules of thumb:

Pronouns tend to come earlier, before longer phrases like heute Abend.
The separable prefix (an) must go to the end of the clause.

You could say Ruf heute Abend an, but once you add mich, Germans will almost always say:

Ruf mich heute Abend an. (natural) not
Ruf heute Abend mich an. (sounds odd, very marked)

Does heute Abend mean this evening or tonight? What about heute Nacht?

heute Abend literally means this evening, i.e. the evening of today.

In English, depending on context, you might translate it as:

this evening (more literal)
tonight (common in everyday speech)

heute Nacht means tonight in the sense of during the night (later, when it’s actually nighttime, usually after you’d say Abend).

So:

Ruf mich heute Abend an. – Call me this evening / tonight (in the evening).
Ruf mich heute Nacht an. – Call me tonight (late at night, after it’s dark and night has started).

Is this sentence formal or informal? Would you say it to your professor or boss?

The sentence is informal because of du and the du-imperative ruf:

Brauchst du Hilfe …, ruf mich … an.

You say this to:

friends
classmates
family
colleagues you’re on du terms with

For a formal version (using Sie) you would say:

Brauchen Sie Hilfe mit dem Stoff, rufen Sie mich heute Abend an.

So you would not normally say the original du-version to a professor or boss unless you are explicitly on du terms with them.