Learn Hardcore German: Es fällt mir manchmal schwer, im Unterricht laut zu sprechen. - Sometimes it is difficult for me to speak loudly in class.

Es is a dummy subject; it doesn’t refer to any specific thing.
The real content of the sentence is the action im Unterricht laut zu sprechen (speaking loudly in class), but German often puts that long zu-infinitive part at the end and uses es at the beginning as a placeholder.
So structurally the sentence is like: Es (it) fällt mir schwer (is hard for me) [to speak loudly in class].

Why is it mir and not mich?

Mir is in the dative case, and the verb fallen in this expression (jemandem schwerfallen) takes a dative object:

Es fällt mir schwer – It is hard for me.
If it were accusative, it would be mich, but this verb pattern does not use accusative. You can remember it as a fixed structure: Es fällt + Dativpronomen + schwer.

How does fallen suddenly mean “to find something difficult”?

Literally fallen means “to fall”, but in the idiom jemandem fällt etwas schwer it has a more abstract sense: “something is hard for someone”.
So:

Es fällt mir schwer = “It is difficult for me / I find it hard.”
You will see the same pattern with other things: Deutsch fällt mir leicht (German is easy for me).

Could I also say Ich finde es manchmal schwierig, im Unterricht laut zu sprechen?

Yes, that is correct and very natural.

Es fällt mir schwer and Ich finde es schwierig express almost the same idea.
The nuance: es fällt mir schwer sounds a bit more like “this is something that doesn’t easily come to me”, while ich finde es schwierig is more of a direct opinion, but in everyday speech they are very close.

Why is there a comma before im Unterricht laut zu sprechen?

That whole part im Unterricht laut zu sprechen is a zu-infinitive clause that depends on schwer (fallen).
German usually separates such clauses with a comma, so the standard written form is:
Es fällt mir manchmal schwer, im Unterricht laut zu sprechen.
According to modern rules, the comma in many zu-infinitive clauses is optional, but here it is strongly preferred and what you will almost always see.

What exactly is im Unterricht? Why not in dem Unterricht?

Im is just the contraction of in dem:

in + dem = im
So im Unterricht literally means “in the lesson / in the class”.
However, Unterricht without an article is also used in a general sense like “class time, lessons”, so im Unterricht is best translated as “in class” rather than “in the specific lesson”.

Why is Unterricht in the dative case here?

The preposition in can take either accusative or dative.

Accusative: movement toward somewhere (into).
Dative: position / location (in, at).
Here we are talking about a situation during class / while in class, i.e. a location in time/space, so in takes the dative: in dem Unterricht → im Unterricht.

Why is laut not changed (no ending like lauten, laute, etc.)?

In im Unterricht laut zu sprechen, laut is used as an adverb, describing how you speak.
Adverbs in German normally do not take endings:

laut sprechen – to speak loudly
schnell laufen – to run quickly
If laut were directly in front of a noun, it could take endings as an adjective (lauter Unterricht), but here it modifies the verb sprechen, so it stays as laut.

Why is zu sprechen at the end? Could I say zu laut sprechen or sprechen zu?

In a zu-infinitive construction, zu goes directly in front of the verb: zu sprechen. That whole infinitive group normally goes to the end of the clause.
The adverb laut belongs in the “middle field” of that group, so you get:

laut zu sprechen, not zu laut sprechen (though zu laut sprechen would mean “to speak too loudly” – different meaning).
Sprechen zu would mean “to address (someone)” in another context, not the infinitive with zu.

Where can manchmal go? Is the word order fixed?

The given sentence Es fällt mir manchmal schwer, … is very natural, but you can move manchmal a bit:

Manchmal fällt es mir schwer, im Unterricht laut zu sprechen.
Es fällt mir schwer, manchmal im Unterricht laut zu sprechen. (slightly different emphasis)
In practice, Manchmal fällt es mir schwer, … and Es fällt mir manchmal schwer, … are the most idiomatic choices.

Can I also say In dem Unterricht fällt es mir manchmal schwer, laut zu sprechen?

Yes, that is grammatically correct.
However, in dem Unterricht here sounds more like you are talking about some specific lesson that both speaker and listener have in mind.
The original im Unterricht is more general: “in class (in general / in class situations)”.

Why is there no article in front of Unterricht (like der Unterricht)?

Unterricht is often used like an uncountable noun meaning “instruction / lessons / class time”, especially with prepositions:

im Unterricht – in class
nach dem Unterricht – after class
When you talk about “the teaching” as a specific session or subject, you might use an article, but in this fixed expression im Unterricht it usually appears without anything extra in front of Unterricht besides the contracted im.

Is there any difference between laut sprechen and laut reden in this context?

Both laut sprechen and laut reden are possible and understandable.
Sprechen is slightly more neutral and is often the safer, textbook choice.
Reden can sometimes sound a bit more informal or conversational, but im Unterricht laut zu reden would still be fine and natural in everyday speech.