Learn Hardcore Finnish: Ennen kuin menen kokeeseen, hengitän rauhallisesti. - Before I go to the exam, I breathe calmly.

Ennen is the adverb meaning before/earlier.
When you want to say before (something happens) using a whole clause (i.e., before I go...), Finnish commonly uses the pattern ennen kuin + clause.

So:

ennen = before
kuin = introduces the comparison/limit point in time, roughly than/that in older logic, but in modern Finnish it’s just part of the fixed conjunction ennen kuin.

You can think of ennen kuin as one unit meaning before (that/when).

Could I drop kuin and just say Ennen menen kokeeseen...?

No. If you want to use a verb clause (I go...), you need ennen kuin.
Without kuin, you must change the structure to a noun/infinitive construction, e.g.:

Ennen koetta hengitän rauhallisesti. = Before the exam, I breathe calmly.
Ennen kokeeseen menoa hengitän rauhallisesti. = Before going to the exam, I breathe calmly. (more formal/explicit)

But Ennen menen... is not grammatical.

Why is there a comma: Ennen kuin menen kokeeseen, hengitän rauhallisesti.?

Finnish typically uses a comma to separate a subordinate clause from the main clause.

Here:

Subordinate clause: Ennen kuin menen kokeeseen
Main clause: hengitän rauhallisesti

So the comma marks the boundary between them. This is standard Finnish punctuation.

What case is kokeeseen, and why is it used?

Kokeeseen is the illative case, meaning into/to something (movement toward and into a place/event).

koe = exam/test
kokeeseen = into the exam / to the exam (illative)

In Finnish, mennä + illative is the usual way to express going to an event or situation:

mennä kouluun = go to school
mennä töihin = go to work
mennä kokeeseen = go to the exam (as an event you enter/participate in)

Does mennä kokeeseen mean physically walking into the exam room, or participating in an exam?

Most commonly it means to go sit/take the exam (participate), not just to head toward the building.

If you specifically mean arriving at a location, you might say things like:

mennä luokkaan = go into the classroom
But mennä kokeeseen is a very natural idiom for going to take an exam.

Why is menen in the present tense if the action is in the future?

Finnish often uses the present tense for near-future actions when the time relationship is clear from context (here: before I go implies a later action).

So menen can mean:

I go (generally)
I am going / I will go (in this context)

If you want to emphasize intention, you can also use a construction like olen menossa (I’m on my way / I’m going), but the present tense is completely normal here.

Why is minä not included? Shouldn’t it be Ennen kuin minä menen... minä hengitän...?

Finnish usually omits subject pronouns because the verb ending already shows the person:

menen = (I) go
hengitän = (I) breathe

You can add minä for emphasis or contrast (e.g., I as opposed to someone else), but it’s not required and often sounds heavier in a neutral sentence.

What form is hengitän, and how is it built?

hengitän is the 1st person singular present of hengittää = to breathe.

Conjugation (present):

minä hengitän
sinä hengität
hän hengittää
me hengitämme
te hengitätte
he hengittävät

So hengitän already contains the meaning I breathe / I am breathing.

What does rauhallisesti do in the sentence, and how is it formed?

rauhallisesti is an adverb meaning calmly. It modifies the verb hengitän (how you breathe).

It’s built from:

rauhallinen = calm (adjective)
adverb ending -sti → rauhallisesti = calmly

This -sti adverb pattern is very common:

nopea → nopeasti (quickly)
varma → varmasti (surely / certainly)

Could the word order be different, like Hengitän rauhallisesti ennen kuin menen kokeeseen?

Yes. Both are natural:

Ennen kuin menen kokeeseen, hengitän rauhallisesti. (sets the time frame first)
Hengitän rauhallisesti ennen kuin menen kokeeseen. (starts with the main action)

Finnish word order is fairly flexible, and moving the time clause often changes what feels most emphasized (time-first vs action-first), but both are grammatical and common.