Learn Hardcore Czech: V parku se ráno smí běhat i pomalu a park je tichý, protože tam zřídka někdo běhá s hlasitou hudbou. - In the park it is allowed to run slowly in the morning and the park is quiet because someone rarely runs there with loud music.

v (in) + static location usually takes the locative case.
The noun park in nominative is park, but the locative singular is v parku.

So:

park (nominative: subject) – Park je tichý.
v parku (locative: where?) – V parku se ráno smí běhat.

Using v park would be ungrammatical in this context.

What exactly does se do in V parku se ráno smí běhat?

Here se creates an impersonal / passive-like construction.

smět = to be allowed / may
smí běhat (without se) would typically mean someone is allowed to run (with a specific subject).
se smí běhat means roughly it is allowed to run / running is allowed (there), with a general, unspecific subject (“one”, “people in general”).

So se turns smí běhat into a general rule about the park, not about some specific person.

Why smí and not může in this sentence?

Both smí and může can be translated as can / may, but:

smět (smím, smíš, smí…) = to be allowed to, about permission or rules.
moci (můžu, můžeš, může…) = to be able / can, covering both possibility and permission, more general.

In a sentence describing what is allowed in the park (like rules or norms), smí is more precise:

V parku se ráno smí běhat… = It is allowed to run in the park in the morning…
Using může would sound more like one can run there (it’s possible) and less like a rule.

What is the difference between běhat and běžet here?

Czech distinguishes imperfective and perfective verbs:

běhat – imperfective, repeated / habitual / ongoing running
běžet – perfective, a single, concrete act of running (or running in progress once)

In this sentence we talk about what people generally do or may do in the park (a regular or possible activity), so the imperfective is used:

smí běhat = they are allowed to run (in general, as an activity)
Not a single event: they are allowed to run once.

If you said smí běžet, it would sound more like they may run (this one time, specific run), which doesn’t fit a general description of the park’s atmosphere.

What does i mean in smí běhat i pomalu?

Here i means roughly also / even.

smí běhat pomalu = they are allowed to run slowly (neutral).
smí běhat i pomalu = they are allowed to run even slowly / also slowly.

The i emphasizes that slow running is included among the allowed ways of running.
It suggests that in some places people might expect you to run fast, but here even slow jogging is fine.

Could the word order be V parku ráno se smí běhat i pomalu? Is it still correct?

Yes, that word order is grammatically correct, but the common, natural pattern follows Czech “2nd position” rules for clitics like se:

In V parku se ráno smí běhat, se is in the second clause position:
- 1st position: V parku (one phrase)
- 2nd position: se

If you say V parku ráno se smí běhat, then the first two elements V parku ráno sound like two separate items before se, which is less typical. Native speakers still understand it, but the usual rhythm wants se early, right after the first phrase.

Other natural options:

Ráno se v parku smí běhat i pomalu.
V parku se smí ráno běhat i pomalu.

All are possible, just slightly different in emphasis.

Why is it just ráno without a preposition? Why not v ráno?

Words like ráno, večer, odpoledne often function as adverbs of time, meaning in the morning, in the evening, in the afternoon by themselves, without a preposition.

So:

Ráno pracuju. = I work in the morning.
Večer čtu. = I read in the evening.

Using v ráno is wrong in standard Czech. You just say ráno to mean in the morning here.

In the sentence, ráno is simply an adverbial of time: when you are allowed to run in the park.

What is the nuance of zřídka někdo běhá? Why is zřídka before někdo?

Zřídka means rarely / seldom. Position affects emphasis:

Zřídka někdo běhá s hlasitou hudbou.
Literally: Rarely does anyone run with loud music.
Emphasis: such people are rare; it almost never happens.
Někdo zřídka běhá s hlasitou hudbou.
Literally: Someone rarely runs with loud music.
Emphasis: a particular person (or some people) rarely do it, but it’s about their habit.

In the original sentence, the speaker wants to say that in that park it almost never happens that anyone runs with loud music. So zřídka in front of někdo fits that meaning.

Why is it někdo and not nikdo after zřídka?

někdo = someone / anyone
nikdo = no one

Zřídka is not a negative word; it’s just a frequency adverb (rarely), so the sentence is not grammatically negative, even if the meaning is “almost never”.

So:

Zřídka někdo běhá… = Rarely does someone/anyone run… (correct)
Nikdo neběhá… = No one runs… (explicit negation)

If you said zřídka nikdo běhá, you would clash two elements: a frequency adverb and a negative pronoun; it would sound very odd or wrong. For strong negation you’d rather say:

Nikdo tam neběhá s hlasitou hudbou. = No one runs there with loud music.

Why is it park je tichý and not park je ticho or park je tiché?

park is a masculine inanimate noun.
The adjective tichý (quiet) must agree in gender, number and case with park.

Forms of the adjective tichý in nominative singular:

masculine inanimate: tichý – park je tichý
feminine: tichá – ulice je tichá (the street is quiet)
neuter: tiché – město je tiché (the town is quiet)

ticho is a noun meaning silence:

V parku je ticho. = There is silence in the park.

Both are possible, but they say slightly different things:

park je tichý = the park (as a place) is quiet.
v parku je ticho = in the park, there is silence.

What does s hlasitou hudbou literally mean, and why is hudbou in that form?

Literally s hlasitou hudbou = with loud music.

s (with) uses the instrumental case.
hudba (nominative) → hudbou (instrumental singular)
hlasitou is the instrumental feminine singular form of hlasitý (loud), agreeing with hudbou.

In Czech, saying běhat s hudbou is natural shorthand for:

running while listening to music (typically with headphones), not physically carrying some object of music.

So běhat s hlasitou hudbou suggests people are running with loud music playing in their ears, the way English might say running with loud music or running while blasting loud music.

Why is there a comma before protože? Could it ever be without a comma?

In standard Czech punctuation, a comma is required before protože when it introduces a subordinate clause:

…, protože tam zřídka někdo běhá s hlasitou hudbou.

You do not normally drop this comma, unlike in English where because can sometimes appear without a comma. The rule is basically:

main clause , protože
- subordinate clause.

So in this sentence, the comma is obligatory in standard writing.