Learn Hardcore Croatian: Stres će proći nakon ispita. - The stress will pass after the exam.

In standard Croatian, the auxiliary će is a clitic and normally goes in the second position in the clause, right after the first stressed word or phrase.
So the neutral order is:

Stres će proći. (Stres = first stressed word → će comes right after it.)

Forms like “Stres proći će” are not standard; će doesn’t usually go at the end like that.
You can say “Proći će stres”, but then the focus tends to be more on the verb (“It will pass, the stress”), with a bit of different emphasis.

What form is proći, and what does it tell us?

Proći is the infinitive of a perfective verb meaning “to pass / to go by / to be over (come to an end)”.
Because it’s perfective, stres će proći means that the stress will be completely over at some point, not that it is just ongoing.
Perfective verbs in the future usually describe a single, completed event.

Could I say “Stres prolazi nakon ispita” instead? What’s the difference?

Yes, you can, but the meaning changes slightly:

Stres će proći nakon ispita. = The stress will be over after the exam (completed, it ends).
Stres prolazi nakon ispita. = The stress passes / goes away after the exam (more like a general statement, using the imperfective verb prolaziti).

The original sentence highlights one future event: after this exam, the stress will end.
The imperfective prolazi sounds more habitual or descriptive, like a general rule.

Why is it nakon ispita and not nakon ispit or nakon ispitu?

The preposition nakon (“after”) always takes the genitive case.
Ispita is the genitive singular of ispit (exam).

Rough declension of ispit (masculine noun):

Nominative: ispit (subject)
Genitive: ispita → used after nakon
Dative: ispitu
Accusative: ispit
Vocative: ispite
Locative: na ispitu
Instrumental: s ispitom

So only nakon ispita is correct here.

Is nakon the same as poslije?

They are very close, and in many contexts you can treat them as synonyms:

nakon ispita
poslije ispita

Both mean “after the exam”, and both take the genitive.
Poslije is slightly more informal and more common in everyday speech; nakon can sound a bit more formal or bookish, but both are perfectly normal.

What case is stres in here, and what gender is it?

Stres is in the nominative singular, because it’s the subject of the sentence.
It is a masculine noun (like many borrowed words in -s: stres, keks, taksij etc.).

So:

Nominative singular: stres
Genitive singular: stresa, etc.

Can stres be plural in Croatian, like “stresses”?

Yes, the plural stresovi exists:

Imam razne stresove na poslu. – “I have various stresses at work.”

However, in many situations Croatian, like English, prefers the uncountable use:

Imam puno stresa. – “I have a lot of stress.”

In your sentence, Stres će proći nakon ispita, it’s used in this general, uncountable sense.

How do I pronounce proći, especially the č and ć?

Approximate pronunciation (IPA): [strês tʃe prɔ̂ːtɕi].

č = like ch in “church” → tʃ
ć = a softer sound, close to the “t” + “y” in “got you” (AmE: gotcha), but palatalized → tɕ

So proći is roughly PROH-tchy, with a softer final -ći than an English “ch”.

Can you give a couple of alternative natural ways to say the same thing?

Some natural variants with slightly different nuance:

Stres će nestati nakon ispita.
– “The stress will disappear after the exam.” (nestati = to disappear)
Bit ćeš opušten/opuštena nakon ispita.
– “You’ll be relaxed after the exam.” (talking directly to someone; opušten for a male, opuštena for a female)
Nakon ispita, sav će stres proći.
– “After the exam, all the stress will pass.” (puts “after the exam” at the start for emphasis)