Learn Hardcore Polish: Krótki spacer często jest lepszy na zmęczenie niż kawa. - A short walk is often better for fatigue than coffee.

masculine: krótki spacer (a short walk)
feminine: krótka kawa (a short coffee – odd meaning, but grammatically correct)
neuter: krótkie okno (a short window)

So:

krótkie spacer – wrong, because krótkie is neuter or plural, but spacer is masculine singular.
krótka spacer – wrong, because krótka is feminine, but spacer is masculine.

Correct is krótki spacer: masculine, singular, nominative – all matching.

Why is it jest lepszy and not jest lepiej?

This is the difference between adjective and adverb:

lepszy = better as an adjective, describing a noun (what kind of thing it is)
- Krótki spacer jest lepszy – A short walk is better (better thing).
lepiej = better as an adverb, describing a verb (how something is done / how someone feels)
- Czuję się lepiej – I feel better.
- On śpi lepiej – He sleeps better.

In the sentence:

Krótki spacer często jest lepszy na zmęczenie niż kawa.

lepszy directly describes the noun spacer (The walk is a better thing for tiredness than coffee), so we must use the adjective form lepszy, not the adverb lepiej.

What exactly does na zmęczenie mean, and why do we use na here?

Na is a very common preposition in Polish. One of its everyday uses is “for / against (as a remedy for)” when talking about illnesses, problems, or symptoms. For example:

tabletki na ból głowy – pills for a headache
herbata na gardło – tea for the throat
krem na trądzik – cream for acne

So na zmęczenie literally means for tiredness, in the sense of to deal with tiredness, against tiredness, as a remedy for feeling tired.

The sentence is saying:
A short walk is often a better remedy for tiredness than coffee.

Which case is zmęczenie in, and why does it look the same as the basic form?

After na in this meaning (for, against – as a remedy), the noun is in the accusative case.

na zmęczenie – for tiredness (accusative)

However, zmęczenie is a neuter noun, and for many neuter nouns:

Nominative singular = Accusative singular

Example pattern:

nominative: zmęczenie – (tiredness)
accusative: zmęczenie – (for tiredness)

So it looks like the basic dictionary form, but in this sentence it is grammatically accusative because of the preposition na.

Why do we say niż kawa and not od kawy? Are both correct in comparisons?

Polish has two common ways to say “better than X”:

[comparative adjective] + niż + nominative
- lepszy niż kawa – better than coffee
[comparative adjective] + od + genitive
- lepszy od kawy – better than coffee

Both are correct and natural, but:

With niż, the compared thing (kawa) stays in nominative.
With od, the compared thing goes into genitive (kawy).

Your sentence uses the niż + nominative pattern:

lepszy niż kawa – better than coffee

It could also be written as:

Krótki spacer często jest lepszy od kawy na zmęczenie.

Same meaning, slightly different structure.

Can I move często somewhere else, like Często krótki spacer jest lepszy… or Krótki spacer jest często lepszy…?

Yes. Polish word order is relatively flexible, and adverbs like często can move around. All of these are grammatically correct:

Krótki spacer często jest lepszy na zmęczenie niż kawa.
Często krótki spacer jest lepszy na zmęczenie niż kawa.
Krótki spacer jest często lepszy na zmęczenie niż kawa.

Differences are mostly about rhythm and emphasis:

Starting with Często emphasizes the frequency: Often, a short walk…
Putting często right before jest (or after it) often sounds a bit more neutral and fluent in speech.

There’s no big change in meaning; all of them say that often a short walk is the better option.

Can I drop jest and say Krótki spacer często lepszy na zmęczenie niż kawa?

In standard, neutral Polish, you normally keep the verb jest when linking a noun with an adjective:

Krótki spacer jest lepszy. – A short walk is better.

Omitting jest can happen in:

headlines, slogans, very informal speech, or certain poetic styles.

For a normal sentence, especially as a learner, you should include it:

Krótki spacer często jest lepszy na zmęczenie niż kawa. – correct and natural
Krótki spacer często lepszy na zmęczenie niż kawa. – feels like a fragment, slogan, or note, not a full standard sentence.

How do I know if kawa here means “coffee in general” or “a cup of coffee”, since there is no article?

Polish has no articles (a, an, the), so kawa can correspond to:

coffee (in general / as a substance)
a coffee / a cup of coffee, depending on context

In this sentence:

…lepszy na zmęczenie niż kawa.

it naturally means coffee in general as a method of dealing with tiredness – better than coffee (as a strategy). If you needed to be very specific, you could add words:

niż filiżanka kawy – than a cup of coffee
niż mocna kawa – than strong coffee

But usually kawa alone is understood from context, just like English coffee can mean both the drink in general or a coffee in everyday speech.

Could I say krótszy spacer instead of krótki spacer? What’s the difference?

Yes, but the meaning changes slightly:

krótki spacer – a short walk (just describes it; no comparison)
krótszy spacer – a shorter walk (compared to some other walk)

Your original sentence:

Krótki spacer często jest lepszy na zmęczenie niż kawa.

focuses on the fact that any short walk (as a type) is often better for tiredness than coffee.

If you said:

Krótszy spacer często jest lepszy na zmęczenie niż długi.
A shorter walk is often better for tiredness than a long one.

then you’d be comparing two kinds of walks (shorter vs longer), not walk vs coffee. So krótki (short) is correct given the intended meaning.

Why is the verb and adjective singular masculine (jest lepszy) even though we might be talking about walks in general?

In Polish, you normally use singular when talking about a type or category in a general statement:

Pies jest wierny. – The dog is faithful. / Dogs are faithful.
Samochód jest drogi. – A car is expensive. / Cars are expensive.

So:

Krótki spacer często jest lepszy na zmęczenie niż kawa.

literally: A short walk is often better for tiredness than coffee,
but just like in English, this also covers the general idea short walks are often better….

If you insisted on plural, you could say:

Krótkie spacery często są lepsze na zmęczenie niż kawa. – Short walks are often better…

Then everything agrees in plural:

krótkie spacery (nom. pl.)
są (3rd person plural)
lepsze (plural adjective)

Both singular and plural are grammatically correct; the singular generic style is very typical for Polish proverbs and general statements.