Learn Hardcore Russian: Время проходит быстро, когда я гуляю в парке. - Time passes quickly when I walk in the park.

проходит – fairly neutral, emphasizes the process of time passing.
идёт – very common everyday wording, also neutral but slightly more colloquial-feeling.
летит – figurative and emotional, used when it feels very fast.

All three are grammatically correct; they just differ in style and emotional color. The original sentence chooses проходит, a neutral, clear choice for learners.

What tense is проходит and why is it present tense if we’re talking about something that feels general or habitual?

Проходит is:

present tense
3rd person singular
imperfective aspect

Russian often uses the present tense of an imperfective verb to express:

general truths:
- Земля вращается вокруг Солнца. – The Earth orbits the Sun.
repeated / habitual situations:
- Я часто читаю вечером. – I often read in the evening.

So Время проходит быстро, когда я гуляю в парке really means:

Time tends to pass quickly whenever I walk in the park.

It’s not about one specific instance, but a general, repeated experience, which is why the present tense is the natural choice in Russian.

Could I put the когда-clause first: Когда я гуляю в парке, время проходит быстро? Does the word order change the meaning?

Yes, both orders are correct:

Время проходит быстро, когда я гуляю в парке.
Когда я гуляю в парке, время проходит быстро.

The basic meaning does not change.

Nuance:

Starting with Время focuses first on time.
Starting with Когда я гуляю в парке focuses first on the situation (walking in the park).

In speech, people choose the order depending on what they want to emphasize, but grammatically both are standard and natural.

Why is there a comma before когда in Russian?

In Russian, когда introduces a subordinate clause of time. Subordinate clauses are almost always separated from the main clause by a comma.

Here:

Main clause: Время проходит быстро
Subordinate clause: когда я гуляю в парке

So the comma before когда is mandatory in standard Russian punctuation:

Время проходит быстро, когда я гуляю в парке.

Why is it в парке and not something like в парк? What case is парке?

Парке is in the prepositional case (предложный падеж).

With в, Russian distinguishes:

Location (where?) – use prepositional case
- гулять в парке – to walk in the park
Direction (where to?) – use accusative case
- идти в парк – to go to the park

In your sentence we talk about being located in the park while time passes, not about going there:

когда я гуляю в парке – when I am walking in the park (location)
so в парке, not в парк.

What is the difference between гуляю and something like погуляю or гуляю по парку?

Гуляю is:

present tense
imperfective aspect of гулять (to walk, to stroll)

Compare:

я гуляю в парке – I am walking / I walk in the park
- ongoing or habitual action
- focus on the process
я погуляю в парке – I will have a walk in the park
- погулять is perfective; я погуляю is future tense
- focus on the completed event, sounds like a plan or promise
я гуляю по парку – I am walking around the park / through the park
- по парку emphasizes movement around/through the area
- в парке emphasizes simply being in the park

In your sentence we want the idea of a general, ongoing activity, so гуляю в парке is the natural choice.

Why is гуляю in the present tense and not something like когда я буду гулять в парке?

Russian often uses present tense + когда for general situations:

Когда я работаю, я слушаю музыку. – When I work, I listen to music.

Когда я гуляю в парке describes a regular, typical situation.

Когда я буду гулять в парке:

uses буду гулять (future of an imperfective verb)
usually refers to a specific future time, e.g.:
- Завтра, когда я буду гулять в парке, позвони мне.
  – Tomorrow, when I am walking in the park, call me.

In your sentence, we’re talking about a general feeling, not a specific future plan, so the simple present гуляю is correct and natural.

Could I drop я and say когда гуляю в парке?

You can sometimes drop я in Russian, but it is less common and more restricted than in some other languages.

Когда я гуляю в парке – fully standard and neutral.
Когда гуляю в парке – can occur in informal speech or stylistically marked texts, but may sound a bit elliptical or poetic.

For a learner, it’s best to keep the pronoun:

Когда я гуляю в парке – this is the safest and most natural version in most contexts.

Why is it быстро and not быстрый? Where does быстро normally go in the sentence?

Быстро is an adverb (how? in what manner?), while быстрый is an adjective (describes a noun).

быстро проходит – passes quickly/fast (modifies the verb)
быстрое время – fast time (describes a noun, and sounds odd in this context)

You need an adverb to describe how the time passes, so быстро is correct.

Typical positions:

Время быстро проходит.
Время проходит быстро.

Both are correct.

Putting быстро directly before the verb may slightly emphasize the manner.
At the end (проходит быстро) is very common and sounds natural here.

What is the gender and case of время here, and why does it look irregular?

Время is:

neuter gender
singular
nominative case (it is the subject of the sentence)

It belongs to a small group of irregular neuter nouns ending in -мя:

время (time)
имя (name)
племя, стремя, пламя, знамя, семя, вымя, темя

Its forms are irregular:

Nom. sg.: время
Gen. sg.: времени
Nom. pl.: времена
Gen. pl.: времён

In your sentence, время is the subject, so nominative is used:

Время (what?) проходит быстро…

Why is it Время проходит (singular) and not something like Времена проходят (plural)?

Время here refers to time as an uncountable, abstract concept – like time in English.

So it is:

singular
neuter
grammatically treated as one whole thing

Времена is the plural form and has different meanings:

historical periods: трудные времена – hard times
seasons or eras, poetically or stylistically

If you said:

Времена проходят быстро, когда я гуляю в парке.

it would sound strange, as if you mean eras or periods of history pass quickly when you walk in the park.

For normal Time passes quickly, use singular время проходит.

How is this sentence pronounced, and where is the stress in each word?

Stress pattern:

Вре́мя – stress on Вре́-
проходи́т – stress on -ди́т
бы́стро – stress on бы́-
когда́ – stress on -да́
я – the single sound ya
гуля́ю – stress on -ля́-
в па́рке – stress on па́-

So approximately:

Вре́мя проходи́т бы́стро, когдá я гуля́ю в пáрке.

(Primary stress marks the syllables in bold here; in actual Russian writing stress is not shown, but correct stress is important for natural pronunciation.)

Is this sentence formal, informal, or neutral in style?

The sentence is neutral in style.

Vocabulary is everyday and standard.
No slang, no special idioms, no official or bureaucratic words.

You can use Время проходит быстро, когда я гуляю в парке in:

spoken conversation
informal writing (messages, emails)
neutral written texts (essays, simple narratives)

It’s appropriate almost anywhere where a neutral tone is acceptable.

Could I say Время летит, когда я гуляю в парке instead? How is that different?

Yes, you can say:

Время летит, когда я гуляю в парке.

Difference:

проходит – neutral: time passes.
летит – figurative and emotional: time flies.

Время летит usually implies:

you are very engaged or happy
time feels especially fast

So:

Время проходит быстро… – Time passes quickly… (neutral observation)
Время летит… – Time flies… (stronger, more emotional)

Both are correct; it’s just a matter of how expressive you want to be.