Mój brat mówi, że pączek z dżemem jest pyszny tylko wtedy, gdy jest jeszcze ciepły.

Mój brat is the subject of the main clause, so it is in the nominative case.

• mój = my
• brat = brother

Both words agree with each other:

• masculine
• singular
• nominative

So mój brat mówi means my brother says.

Mówi is the 3rd person singular present tense of mówić.

In different contexts, mówi can mean:

• says
• is saying
• speaks

In this sentence, because it is followed by a whole clause introduced by że, the best meaning is says:

• Mój brat mówi, że... = My brother says that...

Polish present tense often covers both English simple present and present continuous, so context decides.

Że introduces a subordinate clause and usually means that.

So:

• Mój brat mówi, że... = My brother says that...

In English, that is often optional:

• My brother says the doughnut is delicious...

But in Polish, że is normally kept.

Because pączek is the subject of the clause że pączek z dżemem jest pyszny..., so it must be in the nominative singular.

• pączek = nominative singular
• pączka = usually genitive singular

Here the structure is:

• pączek ... jest pyszny
• the doughnut ... is delicious

Since the doughnut is the thing being described, nominative is required.

Because the preposition z meaning with takes the instrumental case.

• dżem = jam
• z dżemem = with jam

So pączek z dżemem literally means a doughnut with jam.

A useful thing to remember is that z can take different cases depending on meaning:

• z + instrumental = with
• z + genitive = from / out of

So here it is definitely the with meaning.

Both pyszny and ciepły are adjectives describing pączek, so they must agree with it.

Since pączek is:

• masculine
• singular
• nominative

the adjectives are also:

• masculine
• singular
• nominative

So:

• pączek jest pyszny
• pączek jest ciepły

If the noun changed, the adjective would change too:

• bułka jest pyszna = the roll is delicious
• pączki są pyszne = the doughnuts are delicious

Because ciepły is an adjective, and here we need an adjective to describe pączek.

• jest ciepły = is warm (describing a masculine noun)
• ciepło is not the right form here

Ciepło is usually:

• an adverb: warmly
• or part of an impersonal expression: Jest ciepło = It is warm

So:

• Pączek jest ciepły = correct
• Pączek jest ciepło = incorrect

Tylko wtedy, gdy means only when.

Literally, it is closer to:

• only then, when

So the sentence says the doughnut is delicious only when it is still warm.

Yes, in many situations you could also say kiedy instead of gdy:

• tylko wtedy, gdy...
• tylko wtedy, kiedy...

Both are understandable. Gdy can sound a little more compact or slightly more formal/written, but in this sentence both work.

Here jeszcze means still.

So:

• jest jeszcze ciepły = it is still warm

This is a very common word, but it has several meanings depending on context, such as:

• still
• yet
• more / another

In this sentence, the still meaning is the right one.

Because there are really two separate statements inside the sentence:

1. pączek ... jest pyszny = the doughnut is delicious
2. (pączek) jest jeszcze ciepły = it is still warm

Each clause needs its own verb.

The subject pączek is not repeated in the second clause because it is already understood, but the verb jest still has to be there.

So Polish is doing the same thing English does here:

• is delicious
• is still warm

Because Polish normally uses commas before subordinate clauses introduced by words like:

• że = that
• gdy = when
• kiedy = when
• bo = because
• ponieważ = because

So in this sentence, both commas are required:

• Mój brat mówi, że...
• ...tylko wtedy, gdy...

Polish comma rules are often stricter than English ones in this area.

Not completely. Polish word order is more flexible than English word order because cases show grammatical relationships.

The version you have is a natural, neutral sentence:

• Mój brat mówi, że pączek z dżemem jest pyszny tylko wtedy, gdy jest jeszcze ciepły.

You can change some parts, but the emphasis changes. For example:

• Mój brat mówi, że pączek z dżemem jest pyszny tylko wtedy, kiedy jest jeszcze ciepły.

That means basically the same thing.

So the sentence is not absolutely fixed, but the given order is very natural and a good model to learn.

A useful English approximation is PON-chek.

A few details:

• ą before cz sounds roughly like on
• cz sounds like English ch in chop, though the Polish sound is a bit harder
• stress in Polish usually falls on the second-to-last syllable, so here it is on pą

So pączek is approximately:

• PON-chek

That is a good practical pronunciation for a learner.