Po długim spacerze mam większy apetyt i chętnie zjem ciepłą kolację.

Because po in the sense of after normally takes the locative case in Polish.

So:

• spacer = a walk
• po spacerze = after the walk

The adjective also has to match the noun:

• długi spacer = a long walk
• po długim spacerze = after a long walk

Here both words change because of the locative singular:

• długi → długim
• spacer → spacerze

So the whole phrase is literally after long walk with the correct Polish case endings.

Spacerze is the locative singular of spacer.

Basic forms:

• nominative: spacer
• locative: spacerze

You often see the locative after certain prepositions, including:

• w = in
• o = about
• na = on/at
• po = after

So:

• o spacerze = about the walk
• po spacerze = after the walk

In this sentence, po requires the locative, which is why you get spacerze.

Większy is the comparative form of wielki / duży and means bigger, greater, or sometimes more depending on context.

So:

• mam apetyt = I have an appetite / I’m hungry
• mam większy apetyt = I have a bigger appetite

In English, we might naturally say I’m hungrier or I have more appetite. Polish often uses większy apetyt in this kind of sentence.

So większy here does not mean physically larger in a literal way only; it works naturally with apetyt.

Yes, but the meaning changes a little.

• mam duży apetyt = I have a big appetite
• mam większy apetyt = I have a bigger appetite

Większy is comparative, so it suggests bigger than before / bigger than usual / bigger because of the walk.

That fits this sentence well:

• Po długim spacerze mam większy apetyt
  = After a long walk, I have a bigger appetite

If you said duży apetyt, it would sound more general and less connected to comparison.

In Polish, subject pronouns are often omitted because the verb ending already shows who the subject is.

Here:

• mam = I have
• zjem = I will eat / I’ll eat

So ja is understood automatically.

You could say:

• Po długim spacerze ja mam większy apetyt...

but that would usually add emphasis, contrast, or emotion. In normal neutral Polish, leaving out ja is more natural.

Chętnie means something like:

• gladly
• willingly
• with pleasure

So:

• chętnie zjem ciepłą kolację = I’ll gladly eat a warm dinner/supper

It does not literally mean want. Compare:

• chcę zjeść = I want to eat
• chętnie zjem = I’d gladly eat / I’d be happy to eat

This is a very common Polish adverb. You can use it with many verbs:

• chętnie pomogę = I’ll gladly help
• chętnie pójdę = I’ll gladly go
• chętnie to zrobię = I’ll gladly do that

Zjem is the future tense of the perfective verb zjeść.

Polish has two important verb aspects:

• jeść = imperfective, to eat
• zjeść = perfective, to eat up / to eat completely / to have eaten

Because perfective verbs do not have a present tense meaning, their present-looking forms usually refer to the future:

• zjem = I will eat / I’ll eat

So:

• jem kolację = I am eating dinner / I eat dinner
• będę jeść kolację = I will be eating dinner
• zjem kolację = I will eat dinner

In this sentence, zjem works well because it expresses a single completed action: eating the meal.

The difference is mainly aspect.

• jeść = imperfective, focuses on the process, habit, or ongoing action
• zjeść = perfective, focuses on completing the action

Examples:

• Jem kolację. = I’m eating dinner.
• Będę jeść kolację. = I’ll be eating dinner.
• Zjem kolację. = I’ll eat the dinner / I’ll have the dinner.

In your sentence, zjem suggests a concrete, complete event: after the walk, I’ll happily eat a warm meal.

Because kolację is the accusative singular of kolacja, and the adjective has to agree with it.

Base forms:

• ciepła kolacja = a warm dinner/supper

After the verb zjem (I’ll eat), the meal is the direct object, so it goes into the accusative:

• zjem ciepłą kolację

Changes:

• ciepła → ciepłą
• kolacja → kolację

This is a very common pattern with feminine singular nouns in -a.

More examples:

• mam kawę = I have coffee
• widzę kobietę = I see a woman
• zjem zupę = I’ll eat soup

Usually kolacja means the evening meal, so depending on the variety of English, it can be translated as:

• dinner
• supper

A useful distinction in Polish is:

• śniadanie = breakfast
• obiad = the main meal of the day, often lunch or dinner depending on culture and schedule
• kolacja = supper / evening meal

So in many contexts, kolacja is best understood as supper or dinner in the evening.

Yes, the word order is natural.

Po długim spacerze mam większy apetyt i chętnie zjem ciepłą kolację. sounds smooth and normal.

Polish word order is more flexible than English, so you could rearrange it for emphasis, for example:

• Mam większy apetyt po długim spacerze...
• Ciepłą kolację chętnie zjem po długim spacerze.

But those versions shift the focus a bit.

The original sentence is good because:

• it starts with the time/context phrase: Po długim spacerze
• then gives the present feeling: mam większy apetyt
• then the natural consequence: i chętnie zjem ciepłą kolację

That structure feels very natural in Polish.

Here i simply means and, joining two closely connected ideas:

• mam większy apetyt
• chętnie zjem ciepłą kolację

So the sentence says:

• After a long walk, I have a bigger appetite and I’ll gladly eat a warm dinner.

You could sometimes use a in Polish to connect clauses, but a often suggests contrast, transition, or a different angle. In this sentence, i is more straightforward and natural because the second part is a direct continuation of the first.

Yes, you could say that, and it would sound natural:

• Po długim spacerze jestem głodniejszy. = After a long walk, I’m hungrier.

But it is not exactly the same nuance.

• jestem głodniejszy = I am hungrier
• mam większy apetyt = I have a bigger appetite

The second one can sound slightly less direct and a bit more focused on desire for food rather than just physical hunger. Both are good Polish, but the original sentence is perfectly natural.

Not always in every possible meaning, but po very often takes the locative, especially in meanings like:

• after
• around
• along
• in search of

Examples:

• po spacerze = after the walk
• po obiedzie = after dinner
• po mieście = around the city

So in your sentence, po długim spacerze follows a very common and important pattern: po + locative.