На горной дороге водительница просит всех молчать и пристёгивать ремни.

Both горной and дороге are in the prepositional case singular (feminine).

• дорога → дороге (fem. noun, prepositional singular)
• горная → горной (fem. adjective, prepositional singular, short‑type ending ‑ой)

The preposition на with the prepositional case is used here to mean “on / along a mountain road” (location). With дорога, Russians normally say на дороге (“on the road”), not в дороге (the latter is either old‑fashioned or means “on the way / in transit” with a different nuance: Я был в дороге два дня = “I was on the road for two days”).

The basic noun phrase is горная дорога (“mountain road”) in the nominative case.
But in the sentence we need a prepositional phrase after на to show location, so both the adjective and noun change form:

• Nominative: горная дорога
• Prepositional (after на): на горной дороге

Russian adjectives always agree with their nouns in gender, number, and case, so горная has to become горной to match дороге.

Both mean “driver”:

• водитель – grammatically masculine, used for a driver in general and also for a male driver.
• водительница – explicitly female driver (feminine noun formed from водитель).

In modern Russian, using водитель for a woman is possible (especially in formal or neutral contexts), but if the speaker specifically wants to emphasize that the driver is a woman, they say водительница. The sentence chooses водительница to make the driver’s gender clear.

The structure is просить + (кого?) + инфинитив = “to ask (someone) to do something.”

• просит – “(she) asks”
• всех – the direct object: “everyone,” in the accusative plural (form is identical to genitive plural)
• молчать – infinitive: “to be silent / to keep quiet”

So literally: “the (female) driver asks everyone to be silent.”
Russian needs an object (кого? – whom?) after просить, so всех is required.

Все and всех are different cases:

• все – nominative plural: “everyone” as the subject of a verb.
  
  • Все молчат. – “Everyone is silent.”
• всех – accusative (and also genitive) plural: “everyone” as the object of a verb.
  
  • Она просит всех молчать. – “She asks everyone to be silent.”

Since in the sentence “everyone” is the one being asked (object of просит), Russian uses the accusative form всех.

Молчать is an imperfective verb meaning “to be silent, keep quiet.” It focuses on the state / process of not speaking.

Замолчать is perfective and usually means “to fall silent, to stop talking (once).”

Here the driver wants everyone to remain quiet, not just to briefly stop talking at a single moment, so молчать (ongoing silence) is natural:

• просит всех молчать – “asks everyone to keep quiet / be quiet.”

If you said просит всех замолчать, it would sound more like “asks everyone to shut up (right now),” focusing on the moment of stopping the noise.

Both are possible, but they have slightly different aspectual nuances:

• пристёгивать ремни – imperfective: can suggest the general action or habit of fastening seatbelts, or an instruction that applies over time.
• пристегнуть ремни – perfective: one complete action – “to fasten the seatbelts (once, to a finished state).”

In this sentence, the driver is giving a general safety instruction on the mountain road—“be quiet and fasten your seatbelts.” Many speakers would actually choose пристегнуть ремни here; пристёгивать ремни can feel a bit more like “(always) fastening your seatbelts” as a rule or ongoing requirement.

So:

• просит пристёгивать ремни – “asks (people) to fasten seatbelts (as a rule / in general).”
• просит пристегнуть ремни – “asks (people) to fasten the seatbelts (right now).”

Yes, you could say:

• просит всех пристегнуться – “asks everyone to fasten their seatbelts (on themselves),” perfective
• просит всех пристёгиваться – imperfective, more like “to be in the habit of fastening themselves in”

Difference in focus:

• пристёгивать ремни – focuses on the belts as objects (“fasten the belts”).
• пристегнуться / пристёгиваться – focuses on the people fastening themselves in.

In everyday speech about seatbelts, пристегнуться (perfective reflexive) is very common:
Пожалуйста, пристегнитесь. – “Please fasten your seatbelts.”
The given sentence simply chooses the non‑reflexive object construction.

Ремень means “belt,” and ремни is its plural (“belts”).

In the context of a car or bus:

• Each person has one seatbelt – a ремень безопасности.
• The driver is addressing everyone, so there are many seatbelts in total.

Therefore, пристёгивать ремни naturally means “fasten (your) belts,” i.e., all the belts belonging to all the passengers.

You could say:

• пристёгивать ремень – “fasten the belt” (one belt, e.g., to one person).
• пристёгивать ремни – “fasten the belts” (all of them collectively).

In everyday speech, context makes it clear that ремни are seatbelts, even without adding безопасности.

Orthographically, Russian allows ё to be written as е in most texts, so you will see both:

• пристёгивать (with ё, phonetic)
• пристегивать (with е, very common in print)

The pronunciation is always with /yo/: [пристЁгивать].

Using ё is clearer for learners because it shows the correct stress and vowel quality. Native texts often write е, but you must still pronounce it as ё in this word.

Yes, that order is grammatically correct:

• На горной дороге водительница просит… – starts with the setting, “On the mountain road, the driver asks…,” emphasizing the location / situation first.
• Водительница на горной дороге просит… – starts with the subject, “The (female) driver, on the mountain road, asks…,” emphasizing who is doing the action, then specifying where.

The basic propositional meaning is the same. Russian word order is quite flexible; changes mainly affect focus and information structure, not core grammar here.

Main stresses (capital letters mark stressed syllables):

• На гОрной дорОге – гОр‑ной, дорО‑ге
• водИтельница – во‑дИ‑тель‑ни‑ца (stress on ‑ди‑)
• прОсит – прО‑сит
• всЕх – one syllable, stressed
• молчАть – молчАть
• и пристЁгивать ремнИ – при‑стЁ‑ги‑вать (stress on ‑стё‑), ремнИ (stress on final ‑ни)

Typical pitfalls:

• Misplacing stress: водителнИца or вОдительница instead of водИтельница.
• Forgetting that written ё (or hidden е in print) is pronounced /yo/: пристЁгивать.
• Stressing рЕмни instead of correct ремнИ.

Yes, you can say:

• водительница просит, чтобы все молчали и пристегнули ремни.

Differences:

• просит всех молчать – more compact, neutral, and common construction with an infinitive.
• просит, чтобы все молчали – uses a subordinate clause; stylistically a bit heavier, can sound more formal or more emotional, depending on context.

Both are grammatically correct. For everyday instructions like in the original sentence, Russian strongly prefers the просить + кого + инфинитив pattern.