У ворот сквера ходит голубь, а на калитке сидит ворона.

Because у normally takes the genitive case.

The noun ворота (gate/gates) is a plural-only noun in Russian, so its dictionary form is already plural. Its genitive plural form is ворот.

So:

• ворота = gate/gates
• у ворот = by the gate / near the gates

This is a very common pattern:

• у дома = by the house
• у окна = by the window
• у ворот = by the gate(s)

Because ворота сквера means the gates of the square/park.

Here сквера is in the genitive singular because it shows possession or relationship:

• сквер = a small public garden / square / park
• ворота сквера = the gates of the park

So у ворот сквера literally means by the gates of the park.

This is the same idea as:

• дверь дома = the door of the house
• крыша гаража = the roof of the garage

Not exactly.

Russian сквер usually means a small public garden, small park, or green square in a town. It is often greener and more park-like than the English word square suggests.

So depending on context, it may be translated as:

• small park
• public garden
• sometimes square

They are both related to entrances, but they are not the same thing.

• ворота = a large gate, often big double gates for entering a yard, park, or property
• калитка = a small gate, usually for a person to walk through

So in this sentence, the pigeon is near the larger entrance area, while the crow is sitting on the smaller gate.

Yes, and here that is exactly the idea.

Ходит often means:

• walks around
• is moving about
• goes back and forth
• wanders around on foot

For birds like pigeons, Russian very naturally uses ходить when they are on the ground moving around. So ходит голубь suggests the pigeon is walking about near the gate.

This is different from:

• идёт = is going in one direction right now
• летит = is flying
• стоит = is standing
• сидит = is sitting/perched

Yes. In Russian, birds very often сидят when they are perched somewhere.

So:

• ворона сидит на калитке = the crow is sitting/perched on the gate

This is completely natural Russian. English often says is sitting or is perched, and Russian uses сидеть for that.

Because the crow is on the gate, not just near it.

• на калитке = on the gate
• у калитки = by the gate / near the gate

Russian chooses the preposition based on the physical relationship:

• у = near, by
• на = on, on top of, attached to the surface/location

Since the crow is perched on the gate, на калитке is the natural choice.

Because in the present tense, Russian normally omits the verb to be.

So Russian says:

• голубь ходит = the pigeon is walking / the pigeon walks
• ворона сидит = the crow is sitting

There is no separate present-tense word for am / is / are in ordinary sentences like this.

Russian word order is flexible, and starting with the location is very common when setting a scene.

Compare:

• У ворот сквера ходит голубь = At the park gates, a pigeon is walking around
• Голубь ходит у ворот сквера = A pigeon is walking around by the park gates

Both are possible, but the version in the sentence puts the location first, which makes it feel more descriptive, like the speaker is painting a picture of the scene.

А often connects two parts with a mild contrast or comparison.

Here it works like:

• while
• whereas
• and meanwhile

So the sentence gives two parallel details:

• near the park gates, a pigeon is walking around
• on the gate, a crow is sitting

Using а makes the second image feel like a contrasting companion image. It is not a strong opposition, but it is more vivid than simple и.

They are both in the nominative singular, because they are the subjects of their clauses.

• голубь = pigeon, nominative singular
• ворона = crow, nominative singular

They are the ones doing the actions:

• голубь ходит = the pigeon walks
• ворона сидит = the crow sits

In Russian, ворота is grammatically plural, but in meaning it often refers to what English would call a gate as a single entrance structure.

So depending on context, ворота can be translated as:

• the gate
• the gates

This is because many gates are physically made of two parts, and Russian treats the whole thing as a plural-form noun.

Yes.

The sentence has two coordinated clauses:

• У ворот сквера ходит голубь
• а на калитке сидит ворона

Russian normally puts a comma before а when it connects clauses like this.