Learn Hardcore Croatian: Razmišljajući o ispitu, vidim da uopće nema razloga za veliki stres. - Thinking about the exam, I see that there is really no reason for big stress at all.

Razmišljajući is an adverbial present participle (in Croatian grammar: glagolski prilog sadašnji) formed from the verb razmišljati (to think).

It usually corresponds to English while ...‑ing / by ...‑ing, so
Razmišljajući o ispitu ≈ While thinking about the exam / Thinking about the exam.
It is indeclinable (it does not change form for gender, number, or case).
It can only be formed from imperfective verbs (like razmišljati, čitati, pisati).

Very important: the subject of Razmišljajući o ispitu must be the same as the subject of the main clause. Here, the implied subject is ja (I):

(Ja) razmišljajući o ispitu, vidim...
I, thinking about the exam, see...

You cannot use this form if you want a different subject (“While he is thinking about the exam, I see that…”). In that case you need a full clause, not Razmišljajući.

Could I say Kad razmišljam o ispitu, vidim da... instead of Razmišljajući o ispitu, vidim da...? Is there any difference?

Yes, you can. For example:

Kad razmišljam o ispitu, vidim da uopće nema razloga za veliki stres.
Dok razmišljam o ispitu, vidim da uopće nema razloga za veliki stres.

These are both very natural and roughly equal in meaning to Razmišljajući o ispitu....

Nuance:

Razmišljajući o ispitu... is a bit more compact and slightly more formal / written.
Kad / Dok razmišljam o ispitu... sounds more like everyday spoken language.

All three versions are correct; it’s mostly a stylistic choice.

Why is it o ispitu and not o ispit? What case is ispitu?

Ispitu is in the locative singular case.

The preposition o meaning about / concerning is followed by the locative:

o ispitu – about the exam
o knjizi – about the book
o prijatelju – about (a) friend

For the noun ispit (exam), the singular forms are roughly:

Nominative: ispit (this is the dictionary form)
Genitive: ispita
Dative: ispitu
Accusative: ispit
Vocative: ispite!
Locative: (o) ispitu
Instrumental: (s) ispitom

So o ispitu is o + locative.
o ispit is simply ungrammatical in standard Croatian.

Could I say o ispita instead of o ispitu?

No, not in standard Croatian when you mean about the exam.

o (about) genitive
(o ispita) is not used with this meaning.
The normal pattern is o
- locative: o ispitu, o filmu, o poslu.

You will sometimes see o with genitive in older texts, dialects, or fixed expressions, but for normal modern usage with the meaning about, you should learn:

o + locative → o ispitu, o životu, o nogometu, etc.

What does uopće add to the sentence? Can I leave it out?

Uopće is an adverb that means roughly at all / absolutely / in any way. It strengthens the negation:

nema razloga – there is no reason
uopće nema razloga – there is absolutely no reason / there is no reason at all

So it adds emphasis.

If you leave it out:

Vidim da nema razloga za veliki stres. – I see that there is no reason for big stress.

That is still fully correct and natural; it’s just less emphatic than with uopće.

Why is razloga in that form? Which case is it, and why is it used with nema?

Razloga is genitive singular of razlog (reason).

Croatian often uses the genitive with negated existence or possession, especially with nema (there is not / does not have):

Ima razlog. – There is a reason. (accusative or nominative depending on analysis)
Nema razloga. – There is no reason. (genitive)

This pattern is very common:

Imam vremena. – I have time. (genitive of quantity, already)
Nemam vremena. – I don’t have time.
Ima nade. – There is hope.
Nema nade. – There is no hope.

So nema razloga literally is (there) has-not of-reason, which we translate naturally as there is no reason.

Could I say Ne postoji razlog za veliki stres instead of Nema razloga za veliki stres?

Yes, you can:

Ne postoji razlog za veliki stres.

This also means There is no reason for big stress.

Nuance:

Nema razloga za veliki stres.
More common, slightly more colloquial and neutral.
Ne postoji razlog za veliki stres.
Sounds a bit more formal or emphatic, like making a logical statement:
“Such a reason doesn’t exist.”

Both are correct; choose based on style.

Why is it za veliki stres? What case is that, and how does za work here?

Za in the sense of for (purpose, motive, benefit) is followed by the accusative case.

za veliki stres – for big stress
(veliki stres is accusative masculine singular)

Here, za veliki stres explains what kind of reason is being denied:

nema razloga za veliki stres
literally: there is no reason for big stress
→ there is no reason to be so stressed / so stressed out.

Other examples with za + accusative:

razlog za radost – reason for joy
tableta za glavobolju – pill for a headache
vrijeme za odmor – time for rest

What is the difference between stres and stresa? When do I use each form?

Stres is the nominative / accusative singular form.
Stresa is the genitive singular form.

You choose based on grammar:

Nominative / Accusative (subject, direct object, or after some prepositions):
- Veliki stres nije dobar. – Big stress is not good. (subject, nominative)
- Imam veliki stres. – I have big stress. (object, accusative)
- za veliki stres – for big stress (za
  - accusative)
Genitive (after some prepositions, quantities, etc.):
- bez stresa – without stress
- puno stresa – a lot of stress
- oslobađanje od stresa – release from stress

In your sentence, za requires accusative, so we get za veliki stres, not za velikog stresa.

Can uopće be placed somewhere else, like vidim da nema uopće razloga za veliki stres? Is that correct?

Yes, you can move uopće, and the sentence is still grammatically correct:

Vidim da uopće nema razloga za veliki stres. – most natural, very common
Vidim da nema uopće razloga za veliki stres. – also possible, slightly stronger focus on reason.
Vidim da nema razloga uopće za veliki stres. – possible but sounds less natural; word order feels a bit heavy.

In practice, the most idiomatic choice is exactly what you have:

uopće nema – at all not-has / does not have at all

Could I put Razmišljajući o ispitu at the end, like Vidim da uopće nema razloga za veliki stres, razmišljajući o ispitu?

You can do that grammatically, but it is less natural in Croatian.

Typical and most natural placements for this kind of participle phrase:

Razmišljajući o ispitu, vidim da uopće nema razloga za veliki stres.
Vidim, razmišljajući o ispitu, da uopće nema razloga za veliki stres. (more marked)

Putting it at the very end risks sounding like a “dangling” participle, especially in longer sentences, even if the subject is technically the same.

So your original order, with Razmišljajući o ispitu at the beginning, is the clearest and most idiomatic.

Why is there a comma after ispitu but no comma before da?

Razmišljajući o ispitu, is an introductory participial phrase (adverbial phrase).
In Croatian, such phrases are normally separated by a comma from the main clause:
- Razmišljajući o ispitu, vidim...
Vidim da uopće nema razloga za veliki stres.
Here da introduces a subordinate clause (what I see: “that there is no reason…”).
In Croatian, we do not put a comma before da in sentences like this:
- Znam da je kasno. – I know that it is late.
- Mislim da je u pravu. – I think that he is right.
- Vidim da uopće nema razloga za veliki stres. – I see that there is absolutely no reason for big stress.

So: comma after the participial phrase, no comma before da in this kind of object clause.