Learn Hardcore German: In jedem Kurs lerne ich etwas Neues. - In every course I learn something new.

in + dative = location / situation (answering wo? – where?)
- In jedem Kurs lerne ich etwas Neues.
- I am in each course (no movement into it).
in + accusative = movement into something (answering wohin? – where to?)
- Ich gehe in jeden Kurs. – I go into every course / I attend every class.

So Kurs is masculine, singular.
Dative masculine singular of jeder is jedem, so we get in jedem Kurs.

What form of jeder is jedem, and how does it decline with Kurs?

The base forms are:

jeder (masculine)
jede (feminine)
jedes (neuter)

For masculine Kurs, the singular forms are:

Nominative: jeder Kurs (every course) – subject
Accusative: jeden Kurs – direct object with verbs like haben, besuchen
Dative: jedem Kurs – after prepositions that take dative, like in (location)
Genitive: jedes Kurses – rather formal/rare

In the sentence, in requires dative → in jedem Kurs.

Is the word order fixed? Can I move parts of the sentence around?

You must respect the German verb-second rule in main clauses: the finite verb (here lerne) has to be in second position, but many other orders are possible for emphasis.

All of these are correct:

In jedem Kurs lerne ich etwas Neues. (focus on in every course)
Ich lerne in jedem Kurs etwas Neues. (more neutral)
Ich lerne etwas Neues in jedem Kurs. (slight focus on something new)
Etwas Neues lerne ich in jedem Kurs. (strong focus on something new)

Rule of thumb:

Exactly one element (subject, object, time phrase, etc.) goes before the verb.
The conjugated verb stays in second position.
The remaining elements can be reordered, depending on emphasis and style.

Why is Neues capitalized?

Neues here is a noun made from an adjective (a nominalized adjective).

The adjective neu = new
Turned into a noun: das Neue / etwas Neues = the new (thing), something new

In German:

All nouns are capitalized.
When an adjective is used without an explicit noun (new instead of new thing), it becomes a noun and is capitalized, and it takes a normal adjective ending.

So Neues is essentially short for etwas Neues (Ding) = something new (thing).

Why do we say etwas Neues and not etwas neu?

etwas Neues means something new (a new thing). Here neu acts like an adjective in front of an (understood) noun:

etwas Neues ≈ etwas Neues Ding = something new

After etwas / nichts / viel / wenig etc., German normally uses this pattern:

etwas Gutes – something good
nichts Interessantes – nothing interesting
viel Schönes – many beautiful things

etwas neu, on the other hand, would not mean something new; it would usually mean “somewhat new / a bit new”, for example:

Das ist etwas neu für mich. – That is a bit new to me.

So to express something new (a new thing) as in the sentence, you need etwas Neues, not etwas neu.

What gender and case is etwas Neues in this sentence, and why does it end in -es?

Grammatically, Neues here is:

Gender: neuter (like das Neue, das Ding)
Case: accusative (direct object of lerne)

Neuter nominative and accusative singular normally take the adjective ending -es in this kind of pattern:

etwas Neues
nichts Gutes
viel Spannendes

So etwas Neues is neuter accusative singular, which explains the -es ending on neu- → Neues.

Why is lerne used instead of studiere?

German distinguishes between lernen and studieren, unlike English to study / to learn:

lernen = to learn, to study (school homework, languages, skills, facts)
- Ich lerne Deutsch. – I’m learning German.
- Ich lerne jeden Tag etwas Neues. – I learn something new every day.
studieren = to study at university (to be enrolled in a degree program)
- Ich studiere Physik. – I’m studying physics (as my major).
- Sie studiert an der Universität. – She is a university student.

“In every course I learn something new” is about acquiring knowledge in each course, so lernen is the natural verb here, not studieren.

What exactly does Kurs mean here? Is it “course” or “class”?

Kurs is closest to English course / class in the sense of an organized set of lessons:

ein Sprachkurs – a language course
ein Tanzkurs – a dance class
ein Online-Kurs – an online course

In the sentence:

In jedem Kurs = In every course / in each class (I take)

It refers to one complete course or class offering, not to a single lesson. A single lesson is usually die Stunde or die Unterrichtsstunde.

Could I say In jedem Unterricht or In jeder Klasse instead of In jedem Kurs?

Not really, at least not with the same meaning and naturalness:

Unterricht is usually uncountable and means instruction / teaching in general.
- natural: Im Unterricht lerne ich viel. – I learn a lot in class.
- In jedem Unterricht sounds odd, because we don’t usually count each instruction like that.
Klasse usually means:
- the group of students (class as a group), or
- grade level at school (Klasse
  = fifth grade).

So:

In jeder Klasse lerne ich etwas Neues. would usually mean
In each grade / with each class (group of students), I learn something new – different idea.

For In every course / in each class I take, Kurs is the natural choice: In jedem Kurs.

Why does the verb come after In jedem Kurs instead of immediately after ich?

German main clauses follow the verb-second rule:

The conjugated verb must be the second element, but the first element can be something other than the subject.

In the sentence:

First element: In jedem Kurs (a prepositional phrase)
Second element: lerne (the conjugated verb)
Then: ich (subject) + etwas Neues (object)

So:

In jedem Kurs lerne ich etwas Neues. ✓ (correct)
In jedem Kurs ich lerne etwas Neues. ✗ (wrong – verb not in 2nd position)

You could also make ich the first element:

Ich lerne in jedem Kurs etwas Neues. – also correct, same verb-second rule.

How would the sentence change if I wanted to say “In all courses I learn something new”?

You would use the plural of Kurs and the plural form of alle in the dative:

In allen Kursen lerne ich etwas Neues.

Breakdown:

alle → dative plural: allen
Kurs → plural: Kurse; dative plural usually adds -n: Kursen

So:

Singular: in jedem Kurs – in every course
Plural: in allen Kursen – in all courses

Can I drop etwas and just say Ich lerne Neues?

Yes, Ich lerne Neues is grammatically correct and means:

I (am) learn(ing) new things.

Nuance:

Ich lerne etwas Neues.
- focuses on at least one specific new thing each time (something new).
Ich lerne Neues.
- more general: I learn new things (in general / regularly).

In your original sentence, etwas Neues sounds very natural because it emphasizes at least one new thing in each course.