Learn Hardcore Croatian: Metro je brz, ali je gužva velika, pa si radije dopustim dugu šetnju kući. - The metro is fast, but it is very crowded, so I rather allow myself a long walk home.

Metro je brz, ali je gužva velika. – fully standard and natural.
Metro je brz, ali gužva je velika. – also correct; just a different word order.
Metro je brz, ali gužva velika. – elliptical, more like spoken shorthand or headline style; in normal speech/writing you usually keep je.

About position: je is a clitic (unstressed word) and in standard Croatian it wants to stand in second position in its clause.

After ali as first element: ali je gužva velika
Or with gužva as first element: ali gužva je velika

You don’t normally say something like ali gužva velika je in standard language, because je wants that early “second position” spot.

Why is it je gužva velika and not je velika gužva? Is there a difference between gužva velika and velika gužva?

Both patterns are possible, but they express slightly different structures:

je gužva velika = subject (gužva) + predicate adjective (velika).
Literal: the crowd is big.
je velika gužva = description of a noun phrase: velika gužva (a big crowd).
You’d more often see this inside some other structure:
- U metrou je velika gužva. – There is a big crowd in the metro.

In your sentence:

ali je gužva velika sounds like simply describing the state: but the crowd is big (there), with slight emphasis on velika as the important information.
ali je velika gužva is also correct: but there is a big crowd. It may sound a bit more like you’re introducing “a big crowd” as a thing that exists there.

Both are fine and quite close in meaning; the original just chooses the “X is Y” pattern (gužva = velika).

What exactly does pa mean in ..., pa si radije dopustim dugu šetnju kući? How is it different from zato or tako da?

Pa is a very common linking word. Here it roughly means “so / and so / and then” with a light sense of consequence:

Metro je brz, ali je gužva velika, pa si radije dopustim dugu šetnju kući.
→ The metro is fast, but it’s very crowded, so I’d rather allow myself a long walk home.

Comparison:

zato / zato
- clause – therefore / that’s why; sounds a bit stronger, more logical:
  - Metro je brz, ali je gužva velika, zato radije idem pješice.
tako da – so that / so / in such a way that; it often introduces a result:
- Metro je brz, ali je gužva velika, tako da radije idem pješice.

Pa is the most neutral and conversational: it simply continues the story with a mild “so / and as a result” feel.

What is the role of si in pa si radije dopustim dugu šetnju kući? Why not just dopustim without si, or se?

Croatian has two common reflexive pronouns:

se – usually accusative (myself, yourself) or general reflexive
si – dative (to myself, for myself)

In dopustiti si nešto, si is dative and literally means “to myself”:

dopustim dugu šetnju kući – I allow a long walk home (neutral, somewhat abstract).
dopustim si dugu šetnju kući – I allow myself a long walk home / I treat myself to a long walk home.

That si adds the idea of personal benefit or indulgence, which is exactly what English expresses with “I let myself / I allow myself”.

You cannot use se here:

✗ dopustim se dugu šetnju – incorrect in standard Croatian.
✓ dopustim si dugu šetnju – correct and idiomatic.

Why is the word order pa si radije dopustim, and not pa radije si dopustim or something else?

Again this is about clitic placement. Both si and je are clitics and like to stand in second position in their clause.

In your clause pa si radije dopustim:

first element: pa
second element (clitic position): si
then: radije dopustim

So:

✓ pa si radije dopustim – correct (clitic is second).
✗ pa radije si dopustim – incorrect in standard Croatian; here si would be third (after pa and radije).

If you start the clause with radije, then si can follow it:

✓ Radije si dopustim dugu šetnju kući.

There too, radije is first, si is second.

What exactly does dopustiti si mean here? Is it like “decide to walk” or something softer?

Dopustiti si nešto literally means “to allow yourself something”, and often has the nuance of:

treat yourself to…
give yourself permission for…
indulge in…

So:

dopustim si dugu šetnju kući
≈ I allow myself a long walk home / I treat myself to a long walk home.

It’s a bit softer and more self‑indulgent than simply:

radije idem pješice kući – I’d rather walk home.

You might also see priuštiti si with a very similar meaning:

priuštim si dugu šetnju kući – I treat myself to a long walk home.

What does radije mean here, and how does it relate to rado or najradije?

Rado is an adverb meaning “gladly / willingly”.
Its comparative and superlative are:

radije – rather / more gladly → I’d rather / I prefer to
najradije – most gladly → preferably / I like most of all to

In your sentence:

radije dopustim si dugu šetnju kući
→ I would rather allow myself a long walk home / I prefer to take a long walk home.

Other examples:

Rado ti pomažem. – I’m glad to help you.
Radije pijem čaj nego kavu. – I’d rather drink tea than coffee.
Najradije ostajem doma. – I most prefer to stay at home.

How do the adjective forms brz, velika, and dugu relate to the nouns metro, gužva, and šetnju?

They all show agreement in gender, number, and (when needed) case.

metro je brz
- metro – masculine singular
- brz – masculine singular nominative
  → The metro is fast.
gužva [je] velika
- gužva – feminine singular nominative
- velika – feminine singular nominative
  → The crowd is big.
dopustim si dugu šetnju
- šetnju – feminine singular accusative (direct object of dopustim)
- the base adjective is dug – “long”
  - fem. nom. sg.: duga
  - fem. acc. sg.: dugu
- so you get dugu šetnju – a long walk in the accusative.

Croatian adjectives must match the noun they describe in gender, number, and case, which is why the endings change.

Why is it kući and not kuću in dugu šetnju kući? What’s the difference?

Kuća = house, home (as a noun).

Two common forms in everyday speech:

kuću – accusative singular of kuća
- Gradim kuću. – I’m building a house.
- Vidim kuću. – I see the house.
- With a preposition of movement: Idem u kuću. – I’m going into the house.
kući – dative/locative singular, but used without a preposition in a very fixed, adverb‑like way to mean “home / (to) home”:
- Idem kući. – I’m going home.
- Vraćam se kući. – I’m coming back home.

In your sentence, dugu šetnju kući is:

literally: a long walk (going) home.

So kući is the natural form with the idea of direction towards home, not focusing on the building as an object.

Why is the present tense used in dopustim? Does it mean a one‑time action or a general preference?

In Croatian, the simple present tense is used for:

Actions happening right now.
Habits, general truths, and preferences – just like English.

In your sentence, it sounds like a habitual preference:

Metro je brz, ali je gužva velika, pa si radije dopustim dugu šetnju kući.
→ The metro is fast, but it’s very crowded, so I tend to / I usually prefer to allow myself a long walk home.

Context will decide whether it’s a one‑off decision (right now) or a description of how you normally behave in that situation; the form itself is just present tense.

There are no words for “the” or “a” here. How do we know if it’s “the metro” or “a metro”, “the crowd” or “a crowd”?

Croatian has no articles like English a / an / the—you infer definiteness from context.

In this sentence:

Metro je brz
→ The metro is fast (we’re talking about the known city metro system, so English naturally uses the).
ali je gužva velika
→ but the crowd is big or it’s very crowded; again, the situation is specific and obvious (in that metro), so English prefers the or rephrases it.

If the context were more generic or indefinite, English might use a instead, but Croatian would still just say metro, gužva without any extra word. The listener relies on context, not on articles, to get “the vs a”.