После ужина мы пойдём гулять по тихой аллее в парке.

Because после requires the genitive case.

• ужин = nominative, the basic dictionary form
• ужина = genitive singular

So:

• после ужина = after dinner
• compare: после работы = after work, после фильма = after the film

This is just a normal case pattern you need to memorize: после + genitive.

Пойдём is the future form of пойти, so it means something like we will go / we’ll set off.

• идём usually means we are going / we’re going now, or sometimes a planned present/future in context
• пойдём emphasizes the start of the action in the future: we’ll go

In this sentence, the idea is that after dinner, we will go out for a walk. So пойдём is very natural.

This is a very common Russian pattern:

verb of motion + infinitive

Here:

• пойдём = we’ll go / we’ll set off
• гулять = to walk / to stroll / to spend time walking

So пойдём гулять literally means something like we’ll go to walk, but in natural English it is we’ll go for a walk or we’ll go walking.

Russian often uses this structure where English uses a single expression:

• пойти поесть = go eat / go have something to eat
• пойти поспать = go sleep
• пойти гулять = go for a walk

In this sentence, гулять means to walk for pleasure, to stroll, or to spend time outdoors walking.

It is not exactly the same as simply идти, which means to go on foot from one place to another.

So:

• идти = to be walking, to go somewhere on foot
• гулять = to walk around for leisure, to stroll, to hang out outside

That is why пойдём гулять sounds like let’s go for a walk, not just let’s go somewhere.

After по, Russian often uses the dative case when talking about movement along, through, or around a place.

So:

• по аллее = along the alley/path
• по тихой аллее = along the quiet alley

Here both words are in the dative singular:

• аллея → аллее
• тихая → тихой

This is a very common pattern:

• по улице = along the street
• по дороге = along the road
• по парку can mean around the park, through the park, depending on context

Because both the adjective and the noun must match in gender, number, and case.

The base form is:

• тихая аллея = a quiet alley/path

But after по, we need the dative singular:

• feminine adjective тихая → тихой
• feminine noun аллея → аллее

So:

• nominative: тихая аллея
• dative: по тихой аллее

This agreement is a basic feature of Russian grammar.

Because here в парке describes location: in the park.

With в, Russian uses different cases depending on meaning:

• в + accusative = motion into somewhere
  
  • в парк = into the park
• в + prepositional = being in somewhere
  
  • в парке = in the park

In this sentence, the path is located in the park, so Russian uses the prepositional case:

• парк → в парке

Both are possible, and the basic meaning stays the same. The difference is mainly one of word order and emphasis.

• по тихой аллее в парке focuses first on the route: along the quiet alley, then adds where it is: in the park
• в парке по тихой аллее first sets the location: in the park, then specifies the route

Russian word order is more flexible than English word order, because the case endings show grammatical relationships.

So the original sentence is natural, but other orders could also work depending on what the speaker wants to emphasize.

Yes. Russian often drops subject pronouns when the verb already makes the subject clear.

• пойдём already means we will go
• so После ужина пойдём гулять... is perfectly natural

Including мы can add a little emphasis or clarity, but it is not required.

So both are correct:

• После ужина мы пойдём гулять...
• После ужина пойдём гулять...

Because only the first verb carries the tense. The second verb is the activity that you go to do.

So in:

• мы пойдём гулять

the tense is in пойдём = we will go and гулять stays as to walk / to stroll

This is similar to English in structures like:

• we want to walk
• we can walk
• we are going to walk

The first verb is the main finite verb, and the second one remains infinitive.

By itself, пойдём гулять can sometimes mean either, depending on context and intonation.

• In a plain statement like this one, it means we will go for a walk
• In conversation, with the right intonation, Пойдём гулять! can mean Let’s go for a walk!

So the same form can be used for:

• future statement
• invitation / suggestion

In your sentence, because of После ужина and the overall structure, it is clearly a future statement.

Not quite. Аллея usually means a path, walkway, or tree-lined avenue, especially in a park or garden.

So in this sentence, аллея is not a regular city street. It is more like a pleasant pedestrian path in the park.

That is why по тихой аллее в парке gives a calm, scenic feeling.

Будем гулять would mean we will be walking / we will spend time walking, focusing more on the activity itself.

But пойдём гулять focuses on the idea of going out / setting off to do that activity.

Compare:

• После ужина мы пойдём гулять.
  After dinner, we’ll go for a walk.

• После ужина мы будем гулять в парке.
  After dinner, we’ll be walking in the park.

Both are possible, but they emphasize slightly different things. The original sentence is very natural when the idea is then we’ll go out walking.