Learn Hardcore German: Der Ton im Film ist leise, deshalb stelle ich die Lautstärke höher. - The sound in the movie is quiet, therefore I turn the volume up.

Film is masculine: der Film in the nominative.
After the preposition in (with a static location: in the film), German uses the dative case: in dem Film → im Film.

You cannot say in der Film, because der is nominative masculine, not dative. For masculine dative singular, you need dem, which contracts with in to im.

Why is it Der Ton and not Den Ton or Dem Ton?

Der Ton is in the nominative case because it’s the subject of the sentence:

Der Ton im Film = The sound in the film (subject)
ist leise = is quiet (predicate)

Case forms for masculine noun Ton (singular):

Nominative: der Ton (subject)
Accusative: den Ton (direct object)
Dative: dem Ton (indirect object / after some prepositions)
Genitive: des Tons

Here, the sound is doing the being-quiet, so it must be nominative → Der Ton.

What is the difference between Ton and Lautstärke in this sentence?

They refer to different but related things:

der Ton = the sound / audio (what you hear in general)
In the context of a film, Ton often means the whole audio track: dialogue, music, effects.
die Lautstärke = the volume level (how loud or quiet the sound is)
This is the setting on your TV, speakers, or player.

So the sentence says:

The sound in the film is quiet (Ton),
therefore I turn up the volume level (Lautstärke).

Why is leise used here, and not something like ruhig or still?

leise describes volume: quiet / low in volume.

Der Ton im Film ist leise. = The sound in the film is quiet.

Other words:

ruhig = calm, not hectic, not noisy (can refer to atmosphere, behavior)
still = silent, very quiet, not moving, not speaking

In the context of audio volume, leise vs. laut (quiet vs. loud) is the standard pair.
So for talking about how loud the film’s sound is, leise is the natural choice.

Is leise an adjective or an adverb here, and why does it not change its ending?

Here leise is a predicate adjective after the verb sein (ist).

Pattern:

Der Ton ist leise. = The sound is quiet.

Predicate adjectives in German:

Stand after verbs like sein, werden, bleiben.
Do not take adjective endings.
Look like the dictionary form: leise, laut, müde, interessant, etc.

So:

Der leise Ton (before a noun → adjective ending -e)
Der Ton ist leise. (after ist → no ending)

What does deshalb mean, and how is it different from weil?

deshalb means therefore / for that reason / so.

Der Ton im Film ist leise, deshalb stelle ich die Lautstärke höher.
= The sound in the film is quiet, therefore I turn up the volume.

weil means because and introduces a subordinate clause:

Ich stelle die Lautstärke höher, weil der Ton im Film leise ist.
= I turn up the volume because the sound in the film is quiet.

Main differences:

deshalb: stays in a main clause, verb remains in second position.
weil: introduces a subordinate clause, where the finite verb goes to the end.

Both express a cause–effect relationship, just from opposite directions:

cause → deshalb → effect
effect → weil → cause

Why is the word order deshalb stelle ich and not deshalb ich stelle?

In a German main clause, the finite verb must be in second position (the V2 rule).

In the second clause:

deshalb is put in position 1 (the “Vorfeld”).
The verb stelle must then be position 2.
The subject ich moves after the verb.

So the correct order is:

deshalb (1) stelle (2) ich (3) die Lautstärke höher

deshalb ich stelle would break the V2 rule and is ungrammatical in standard German.

Why is it die Lautstärke here, and which case is it in?

die Lautstärke is in the accusative case because it is the direct object of the verb stellen.

ich = subject (nominative)
stelle = verb
die Lautstärke = direct object (accusative)
höher = how I set it (a complement)

For feminine nouns in the singular, the article die is the same in nominative and accusative:

Nominative: die Lautstärke (as subject)
Accusative: die Lautstärke (as object)

So you cannot tell nominative vs. accusative from the form here; you see it from the function in the sentence.

What does the phrase die Lautstärke höher stellen literally mean?

Literally, it is:

die Lautstärke = the volume
höher = higher
stellen = to set, to put, to adjust (to a position)

So die Lautstärke höher stellen = to set the volume higher, i.e. to turn up the volume.

In German, stellen is commonly used for changing settings:

die Temperatur höher stellen = turn the temperature up
den Wecker auf 7 Uhr stellen = set the alarm to 7 o’clock
die Lautstärke leiser stellen = turn the volume down

Why is it höher and not something like mehr hoch?

höher is the comparative form of the adjective hoch (high).

Forms of hoch:

Positive: hoch (high)
Comparative: höher (higher)
Superlative: am höchsten (highest)

German does not form comparatives with mehr + adjective in normal cases.
You don’t say mehr hoch; you must use the comparative ending -er → höher.

So:

Ich stelle die Lautstärke höher. = I set the volume higher.

Could I also say Ich mache die Lautstärke höher or Ich mache die Lautstärke lauter? Are those correct?

Ich mache die Lautstärke lauter is natural and correct.

lauter = comparative of laut (loud → louder)
Literally: I make the volume louder.

Ich mache die Lautstärke höher is understandable, but it sounds less natural.
Usually:

You stellen or erhöhen a Lautstärke or a level.
You machst etwas lauter/leiser (you make something louder/quieter).

More idiomatic options:

Ich stelle die Lautstärke höher.
Ich mache den Ton lauter.
Ich drehe die Lautstärke höher / lauter. (colloquial: turn the volume up)

Can I say Der Ton im Film ist leise, deshalb mache ich den Fernseher lauter instead? Does it mean the same?

Yes, that is correct and natural:

Der Ton im Film ist leise, deshalb mache ich den Fernseher lauter. = The sound in the film is quiet, therefore I make the TV louder.

The meaning is practically the same:

Original: you explicitly adjust the volume setting (die Lautstärke).
Alternative: you make the TV louder, which in practice also means increasing its volume.

Both sound fine; they just focus on different “objects” (the volume level vs. the device).

Why is the verb stelle in the present tense (stelle ich) instead of a future form?

German often uses the present tense to talk about immediate or near-future actions, especially when the context makes the time clear.

Here, the situation is:

The sound is quiet now,
so I now (or in a moment) turn up the volume.

English might also use present: The sound is quiet, so I turn up the volume (describing what you are doing right now).

A future form like ich werde die Lautstärke höher stellen would sound like you’re planning it for later. The simple present stelle ich is the most natural here.

Could I say Der Ton im Film ist leise, deshalb stelle ich die Lautstärke lauter instead of höher?

Yes, that is also grammatically correct:

… deshalb stelle ich die Lautstärke lauter.

Here you use:

lauter = comparative of laut (loud → louder)

Subtle nuance:

höher stellen focuses on the level (set it to a higher level/number).
lauter stellen focuses more on the perceived loudness (louder).

Both are used in everyday language and would be understood the same way in this context.