Learn Hardcore German: Das Sprechen im Kurs fällt mir noch schwer. - Speaking in the course is still difficult for me.

Sprechen is capitalized because it is being used as a noun, not as a verb.
German often turns infinitive verbs into nouns to talk about the activity in general.

sprechen = to speak (verb)
das Sprechen = speaking / the act of speaking (noun)

So das Sprechen im Kurs means speaking in class or the act of speaking in the course.

Why do we have das before Sprechen? Is it just the definite article “the”?

Yes, das is the neuter definite article “the”, but here it’s also a signal that an infinitive is being used as a noun.

Infinitives used as nouns in German are always neuter and usually take das:

das Essen – eating / the food
das Lesen – reading
das Sprechen – speaking

So das Sprechen = “the speaking” → more naturally in English: speaking.

What does fällt … schwer literally mean, and why is fallen used to express difficulty?

Literally, fallen means “to fall”.
The expression jemandem fällt etwas schwer literally is “something falls heavy to someone”, which idiomatically means “something is difficult for someone” or “someone finds something hard”.

So:

Das Sprechen im Kurs fällt mir schwer.
= Speaking in class is hard for me / I find speaking in class difficult.

It’s a common idiomatic pattern:

Mathe fällt ihm leicht. – Math is easy for him / He finds math easy.

How does the structure jemandem fällt etwas schwer work in terms of grammar and cases?

The pattern is:

etwas (the thing that is difficult) → nominative subject
jemandem (the person who experiences the difficulty) → dative object
schwer → adjective describing how it “falls”

In the sentence:

Das Sprechen im Kurs = nominative subject (what is difficult)
mir = dative (to me)
fällt … schwer = “is difficult”, literally “falls heavy”

So it’s not I who is the grammatical subject; the activity is the subject.

Why is it mir and not mich?

Mir is the dative form of ich, and the expression jemandem fällt etwas schwer always takes dative for the person.

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

Because the structure is “something falls heavy to someone”, German uses the dative:

Das fällt mir schwer. – That is hard for me.
Ihm fällt Deutschlernen schwer. – Learning German is hard for him.

Using mich would be ungrammatical here.

What exactly does noch add to the meaning?

Noch here means “still” in the sense of “not yet no longer difficult”.

fällt mir schwer = is difficult for me
fällt mir noch schwer = is still difficult for me / is still hard (but I expect it to get better)

So noch suggests:

The difficulty has been there for some time.
There is an expectation or hope that it will change in the future.

What’s the difference between schwer and schwierig in this context?

Both can mean “difficult”, and in many contexts they overlap.

schwer literally = “heavy”; figuratively “hard, tough”
schwierig = “complicated, problematic, difficult”

In the fixed expression jemandem fällt etwas schwer, you must use schwer, not schwierig:

Das Sprechen im Kurs fällt mir schwer. ✅
Das Sprechen im Kurs fällt mir schwierig. ❌ (wrong)

Outside this idiom, both are often possible, with schwer sounding a bit more like “hard” and schwierig more like “complicated”.

What does im Kurs mean exactly, and why is it dative?

Im is the contraction of in dem:

in
- dem = im

Kurs is a masculine noun (der Kurs).
After in with a location (“where?” not “where to?”), German uses the dative case:

Wo? – im Kurs (in the course / in class)

So im Kurs = in class or in the course, in the sense of during the lesson / during the course sessions.

Why is the word order fällt mir noch schwer and not something like fällt noch mir schwer?

German has relatively flexible word order, but some patterns are much more natural.

In the verbal bracket fällt … schwer, what goes between verb and adjective is usually:

pronoun objects (like mir)
adverbs (like noch)

So:

fällt mir noch schwer (very natural)
fällt noch mir schwer (sounds odd and somewhat marked)
fällt mir schwer noch (unusual and wrong in standard usage)

Placing the short pronoun mir early is typical; adverbs like noch usually come after pronouns.

Can I say Das Sprechen im Kurs ist noch schwer für mich instead? Is it correct?

Yes, that sentence is grammatically correct and understandable:

Das Sprechen im Kurs ist noch schwer für mich.

It means the same overall: “Speaking in class is still hard for me.”

However, native speakers much more commonly use the idiom:

Das Sprechen im Kurs fällt mir noch schwer.

The fällt mir noch schwer version sounds more natural and idiomatic, especially when talking about skills and abilities.

Can I say Im Kurs zu sprechen fällt mir noch schwer instead of Das Sprechen im Kurs fällt mir noch schwer?

Yes, that is also correct:

Im Kurs zu sprechen fällt mir noch schwer.

Both mean essentially the same thing:

Das Sprechen im Kurs … → focuses on “the speaking in class” as a noun phrase.
Im Kurs zu sprechen … → uses an infinitive zu sprechen (“to speak”) with a prepositional phrase im Kurs.

Both are natural. The das Sprechen version feels slightly more compact and nominal; the zu sprechen version highlights the action more as a verb-like idea.