Learn Hardcore German: In der nächsten Probe im Proberaum wollen sie etwas Kompliziertes langsamer spielen. - In the next rehearsal in the rehearsal room they want to play something complicated more slowly.

Here we are talking about when/where something will happen: in der nächsten Probe = “during/at the next rehearsal”, so you need dative (der).

In die nächste Probe would describe movement into the rehearsal, something like “(going) into the next rehearsal”, which doesn’t fit the meaning here.

Could you also say bei der nächsten Probe instead of in der nächsten Probe? What’s the difference?

Yes, bei der nächsten Probe is also possible and very natural.

in der nächsten Probe focuses a bit more on what happens during the actual rehearsal situation itself (during the playing, practising, etc.).
bei der nächsten Probe is more like “on the occasion of the next rehearsal / when we next rehearse”.

In many contexts both work and the difference is very small; speakers choose largely by habit and nuance.

Why is it der in in der nächsten Probe and not dem?

The noun Probe is feminine in German:

Nominative: die Probe
Accusative: die Probe
Dative: der Probe
Genitive: der Probe

dem is the dative article for masculine/neuter nouns, not feminine ones.
Since in here requires dative (location) and Probe is feminine, you get in der Probe → in der nächsten Probe.

Why does the adjective appear as nächsten and not nächste in in der nächsten Probe?

This is about adjective endings. After a definite article (der, die, das) you normally use the weak set of endings.

For feminine dative singular, the weak ending is -en:

der nächsten Probe (feminine, dative, weak ending -en)

So:

die nächste Probe (nominative)
in der nächsten Probe (dative)

nächste would be correct in nominative (die nächste Probe), but here we’re in the dative, so nächsten is required.

What exactly does im Proberaum mean, and why is it im instead of in dem?

im is just the standard contraction of in dem:

in (in) + dem (dative masculine/neuter article) → im

Proberaum (rehearsal room) is masculine:

Dative: in dem Proberaum
Contracted: im Proberaum

So im Proberaum literally means “in the rehearsal room” and is just a shorter, more natural way to say in dem Proberaum.

What is the difference between Probe and Proberaum?

die Probe = the rehearsal itself, the practice session as an event.
- In der nächsten Probe = “in/during the next rehearsal (session)”.
der Proberaum = the physical space where rehearsals take place, the rehearsal room.
- im Proberaum = “in the rehearsal room”.

So the sentence talks both about the event (Probe) and the place (Proberaum).

Why does the sentence start with In der nächsten Probe im Proberaum instead of Sie wollen …?

German main clauses obey the verb-second rule: the conjugated verb must be in second position, but any single constituent can be put in first position.

Here, the whole chunk In der nächsten Probe im Proberaum is treated as one “slot” (one constituent) in first position, so the finite verb wollen must come second:

In der nächsten Probe im Proberaum | wollen | sie …

This fronting puts extra emphasis on the time/place.
You could also say the more neutral:

Sie wollen in der nächsten Probe im Proberaum etwas Kompliziertes langsamer spielen.

Both are correct; the original simply highlights when/where.

How do we know what sie means here (they / she / formal you)?

There are three possibilities in German:

sie (lowercase) = she or they
Sie (capital S) = you (formal, singular or plural)

We can narrow it down with the verb form:

3rd person singular: sie will = “she wants”
3rd person plural: sie wollen = “they want”

The sentence has wollen, so it must be 3rd person plural → they.

It’s not the formal Sie, because that form is always written with capital S even in the middle of a sentence, and here it’s lowercase.

Why do we have wollen … spielen instead of just spielen?

wollen is a modal verb meaning “to want (to)”. The construction wollen + infinitive expresses intention:

Sie spielen etwas Kompliziertes langsamer.
= They play / are playing something complicated more slowly.
Sie wollen etwas Kompliziertes langsamer spielen.
= They want to play something complicated more slowly.

So wollen … spielen adds the idea of wanting / planning to do it, rather than just stating that they play it.

Why is etwas Kompliziertes capitalized, and why does Kompliziertes end in -es?

etwas means “something”. When you put an adjective after etwas, nichts, viel, wenig etc., the adjective often becomes a noun-like word (a nominalized adjective) meaning “something [adjective]”:

etwas Neues – something new
nichts Gutes – nothing good
viel Interessantes – many interesting things
etwas Kompliziertes – something complicated (a complicated thing)

Because it’s being used as a noun, Kompliziertes is capitalized.
The ending -es is the normal neuter strong ending in this pattern after etwas.

Why is langsamer at the end of the sentence, and what form is it?

langsamer is the comparative form of the adjective/adverb langsam (“slow”) and here it is used as an adverb: “more slowly”.

In a clause with a modal verb, German forms a sentence bracket:

finite verb second: wollen
other verb at the end: spielen

Adverbs like langsamer are usually placed near the main verb, so the natural order is:

… wollen sie etwas Kompliziertes langsamer spielen.

You could also say:

… wollen sie langsamer etwas Kompliziertes spielen.

Both are grammatically correct; the given version keeps langsamer directly next to spielen, which is very typical. You cannot put spielen earlier because with a modal, the main verb must stay at the end.