Learn Hardcore German: Nach dem Frühstück nervt das Chaotische im Zelt die Kleinen. - After breakfast the chaotic stuff in the tent annoys the little ones.

Nach dem Frühstück – time phrase (After breakfast)
nervt – verb (annoys)
das Chaotische im Zelt – subject (the chaotic mess / the chaotic stuff in the tent)
die Kleinen – object (the little ones / the small children)

So grammatically:

Subject (nominative): das Chaotische im Zelt
Verb: nervt (3rd person singular)
Direct object (accusative): die Kleinen

You can see that das Chaotische is singular (takes das) and the verb is singular (nervt, not nerven), so that must be the subject. Die Kleinen is plural, and here it is in the accusative plural.

Why is Chaotische capitalized and what does it mean exactly?

Chaotische is originally an adjective meaning chaotic. In this sentence it has been nominalized (turned into a noun):

das chaotische Zelt – the chaotic tent (adjective before a noun)
das Chaotische – the chaotic thing / the chaotic stuff / the chaos (adjective used as a noun)

When German turns an adjective into a noun like this, it:

Takes an article (das, der, die, ein, etc.)
Is written with a capital first letter
Still gets adjective endings (here -e: Chaotische)

So das Chaotische in context means something like the chaotic stuff, the messiness, or more freely: the chaos.

What does die Kleinen mean, and why is Kleinen capitalized?

die Kleinen literally means the small ones, and in context usually the little ones, i.e. the little children.

Again, this is a nominalized adjective:

kleine Kinder – small children
die kleinen Kinder – the small children
die Kleinen – the little ones

Because Kleinen is being used as a noun (and not followed by a noun), it is:

Capitalized
Used with an article (die)
Given an adjective ending (-en for plural)

So die Kleinen here is a short way of saying die kleinen Kinder.

Why is the verb nervt and not nerven?

The infinitive is nerven (to annoy). In the present tense:

ich nerve
du nervst
er / sie / es nervt
wir nerven
ihr nervt
sie / Sie nerven

The subject is das Chaotische im Zelt, which is 3rd person singular neuter (because of das), so the verb must be nervt (3rd person singular), not nerven.

If the subject were plural, the verb would be nerven:

Die Unordnung und die Lautstärke im Zelt nerven die Kleinen.
(The mess and the noise in the tent annoy the little ones.)

How does the verb nerven work in German? Is it like English to nerv(e)?

nerven means to annoy, to get on someone’s nerves. The pattern is:

etwas nervt jemanden
something annoys someone

Example:

Das Chaotische im Zelt nervt die Kleinen.
The chaotic mess in the tent annoys the little ones.

Other useful forms:

jemanden nerven – to annoy someone
Das nervt! – That’s annoying! / That gets on my nerves!
Ich bin genervt. – I’m annoyed.

You can also say:

Das geht den Kleinen auf die Nerven. – That gets on the little ones’ nerves.

But in this sentence, nerven is a straightforward transitive verb: subject annoys object.

Why is it Nach dem Frühstück and not Nach das Frühstück?

The preposition nach always takes the dative case when it means after (in time):

nach der Arbeit – after work
nach der Schule – after school
nach dem Essen – after the meal
nach dem Frühstück – after breakfast

Frühstück is neuter:

Nominative: das Frühstück
Dative: dem Frühstück

Because of nach + dative, we must say nach dem Frühstück.

What is im Zelt, and why not in das Zelt?

im is a contraction of in dem:

in dem Zelt → im Zelt

Here im Zelt answers Where? (location), so German uses dative case:

Wo ist das Chaotische? – Im Zelt.
Where is the chaotic stuff? – In the tent.

For location:

in
- dative: in dem Zelt / im Zelt – in the tent (being inside)

For direction (movement into):

in
- accusative: in das Zelt – into the tent (going into it)

In this sentence we’re talking about the mess inside the tent (location), not moving into it, so im Zelt (dative) is correct.

Does im Zelt belong to das Chaotische or to die Kleinen?

As written:

Nach dem Frühstück nervt das Chaotische im Zelt die Kleinen.

The most natural reading is:

das Chaotische im Zelt = the chaotic stuff in the tent (subject)
die Kleinen = the little ones being annoyed (object)

So im Zelt is part of the subject phrase:

[das Chaotische im Zelt] nervt [die Kleinen].

If you wanted die Kleinen im Zelt (the little ones in the tent), you would normally place im Zelt directly after die Kleinen:

Nach dem Frühstück nervt das Chaotische die Kleinen im Zelt.
After breakfast, the chaotic stuff annoys the little ones in the tent.

Word order and spoken emphasis decide which noun phrase im Zelt attaches to.

Could I also say Das Chaos im Zelt nervt die Kleinen instead of das Chaotische im Zelt?

Yes, that’s perfectly correct and probably more common in everyday speech:

Das Chaos im Zelt nervt die Kleinen.

Differences:

das Chaotische – stylistically a bit more abstract or “literary”; focuses on the chaotic aspect, the messiness
das Chaos – very common noun; straightforward chaos / mess

Meaning-wise, in this context they are almost the same: the mess in the tent annoys the little ones.

Why is die Kleinen in the accusative if it looks the same as nominative plural?

For plural die-words, nominative and accusative both look like die:

Nominative plural: die Kleinen
Accusative plural: die Kleinen

So form alone does not tell you the case here. You identify subject vs object by:

The other noun phrase: das Chaotische is neuter singular, clearly nominative because of das and because the verb is singular (nervt).
The verb agreement: nervt is 3rd person singular, so the subject must be singular das Chaotische im Zelt, not plural die Kleinen.
The semantics: it makes more sense that the mess annoys the children, not the other way around.

In short, die Kleinen here is accusative plural, but its form is identical to nominative plural.

Can I move parts of the sentence around? For example, can I say Das Chaotische im Zelt nervt die Kleinen nach dem Frühstück?

Yes. In German main clauses, the finite verb must be in second position, but other elements can move. All of these are correct and mean practically the same:

Nach dem Frühstück nervt das Chaotische im Zelt die Kleinen.
Das Chaotische im Zelt nervt nach dem Frühstück die Kleinen.
Das Chaotische im Zelt nervt die Kleinen nach dem Frühstück.

Differences:

Version 1 emphasizes the time (After breakfast).
Version 2 emphasizes the subject (The chaotic stuff in the tent).
Version 3 may put slightly more focus at the end on after breakfast, but still OK.

The key rule: exactly one constituent before the conjugated verb (nervt). Everything else can move behind it.

Does nervt here mean annoys or is annoying? How does German express the progressive?

German present tense covers both:

Das Chaotische im Zelt nervt die Kleinen.

can be translated as:

The chaotic mess in the tent annoys the little ones.
The chaotic mess in the tent is annoying the little ones.

Standard German normally does not require a separate progressive form. Context tells you whether it is:

a general/regular fact, or
an action happening now or in a specific situation.

If you really want to emphasize right now, you might add an adverb:

Gerade nervt das Chaotische im Zelt die Kleinen. – Right now, the mess in the tent is annoying the little ones.

Why is it das Chaotische and not der Chaotische or die Chaotische?

The choice of das / der / die with a nominalized adjective reflects gender and number that the speaker has in mind:

das Chaotische – neuter singular, very abstract or collective:
the chaotic thing / the chaotic stuff / the chaos (as a whole)
der Chaotische – masculine singular:
could mean the chaotic man/person (context needed)
die Chaotische – feminine singular:
could mean the chaotic woman/person

Here we are not talking about a person, but about an abstract quality or mass (the mess), so neuter das Chaotische fits best.

If you wanted to stress many different chaotic things, you could theoretically say die Chaotischen (plural), but that sounds unusual in this context; most speakers would just use das Chaos or die Unordnung instead.