Как ни тихо в сквере утром, у калитки всё равно сидит ворона.

This is a common Russian concessive pattern:

как ни + adverb/adjective, ... всё равно ...

It means something like:

• no matter how ...
• however ...
• even though it is ...

So Как ни тихо в сквере утром, ... means:

• No matter how quiet it is in the square in the morning, ...

This structure often sets up a contrast with the main clause.

Examples:

• Как ни старайся, ничего не выходит. — No matter how hard you try, nothing works out.
• Как ни интересно, я уже устал. — However interesting it is, I’m already tired.

In your sentence, the idea is: Even if the square is very quiet in the morning, there is still a crow sitting by the gate.

Because ни is part of a fixed concessive pattern: как ни...

Here ни does not simply negate the word. Instead, it helps create the meaning no matter how or however.

Compare:

• не usually gives ordinary negation:
  • не тихо = not quiet
• ни in this pattern gives a concessive meaning:
  • как ни тихо = no matter how quiet

So как ни тихо does not mean how not quiet. It is a set structure that learners should memorize as a whole.

Because тихо is the short-form adverb/predicative form meaning quietly or, in sentences like this, it is quiet.

Here Russian is describing a state of the place:

• В сквере тихо. — It is quiet in the square.

That is why Russian uses тихо, not the adjective тихий.

Compare:

• тихий сквер — a quiet square
  Here тихий describes the noun сквер.
• в сквере тихо — it is quiet in the square
  Here тихо describes the situation/environment.

So in Как ни тихо в сквере утром, Russian is saying however quiet it is in the square in the morning.

В сквере is prepositional case.

The preposition в can take different cases depending on meaning:

• в + accusative = motion into something
  
  • в сквер — into the square
• в + prepositional = location in something
  
  • в сквере — in the square

Here the sentence is about location, not movement, so Russian uses the prepositional:

• в сквере

This is exactly like:

• в парке
• в доме
• в комнате

Russian often uses the instrumental case for parts of the day when talking about when something happens.

So:

• утром = in the morning
• днём = in the daytime / during the day
• вечером = in the evening
• ночью = at night

This is very common and should mostly be learned as a time expression.

Examples:

• Я работаю утром. — I work in the morning.
• Вечером было холодно. — It was cold in the evening.

So в сквере утром simply means in the square in the morning.

У калитки means by the gate or near the gate, and калитки is genitive singular.

The preposition у usually takes the genitive and often means:

• by
• near
• at
• sometimes at the home/place of

Examples:

• у дома — by the house
• у окна — by the window
• у дороги — by the road

So:

• dictionary form: калитка
• after у: у калитки

Also, калитка is usually a small gate or garden gate, not a large main gate.

Всё равно means something like:

• all the same
• still
• anyway
• nevertheless

In this sentence, it reinforces the contrast introduced by как ни:

• Как ни тихо ..., всё равно ...
• No matter how quiet ..., still ...

So the structure is:

1. concessive idea: however quiet it is
2. main fact that remains true: there is still a crow sitting by the gate

This pairing is very natural in Russian.

Other examples:

• Как ни спеши, всё равно опоздаешь. — No matter how much you hurry, you’ll still be late.
• Как ни красиво здесь, всё равно хочу домой. — No matter how beautiful it is here, I still want to go home.

Because the subject is ворона, which is singular:

• ворона = crow
• сидит = sits / is sitting

If it were plural, you would have:

• сидят вороны — crows are sitting

Russian present tense verbs agree with the subject in number and person, so:

• ворона сидит
• вороны сидят

Russian word order is flexible, and the final position often gives a word special communicative focus.

The neutral/basic idea might be:

• У калитки всё равно сидит ворона.

Putting ворона at the end can make it sound a bit more like:

• there is still a crow sitting by the gate
• with focus on the crow as the noteworthy element

So the sentence flow is roughly:

1. set the scene: however quiet it is in the square in the morning
2. give the contrasting fact: by the gate there is still a crow

This kind of word order is very natural in descriptive or literary Russian.

Russian often does not need a direct equivalent of English there is / there are in the present tense.

English:

• There is a crow by the gate.

Russian:

• У калитки сидит ворона.

Russian simply uses the location plus the verb and noun. The idea of existence/presence is understood from the structure.

Compare:

• На столе книга. — There is a book on the table.
• В комнате стоит стул. — There is a chair in the room.
• У калитки сидит ворона. — There is a crow sitting by the gate.

So Russian usually expresses this without a present-tense to be.

Either can work, depending on context.

Russian present tense often covers both:

• sits
• is sitting

So сидит ворона can mean:

• a crow sits
• a crow is sitting

In this sentence, is sitting often sounds more natural in English because it describes a scene.

Russian does not require a special progressive form the way English often does.

Not exactly.

Сквер usually means a small public garden, square, or small landscaped park area, often in a town or city.

Парк usually means a larger park.

So:

• сквер = smaller, often urban, more like a public square with trees/benches
• парк = larger park

A learner should understand в сквере as something like:

• in the square
• in the small park
• in the public garden

The best English choice depends on context.

Because Как ни тихо в сквере утром is a subordinate concessive clause, and it is followed by the main clause:

• Как ни тихо в сквере утром,
• у калитки всё равно сидит ворона.

Russian normally separates this kind of subordinate clause with a comma.

So the structure is:

• subordinate clause: however quiet it is in the square in the morning
• main clause: there is still a crow sitting by the gate

Yes. Russian allows several close variants, though the style or emphasis changes.

For example:

• Как ни тихо утром в сквере, у калитки всё равно сидит ворона.
• Как бы тихо ни было в сквере утром, у калитки всё равно сидит ворона.

The second version, with как бы ... ни было, is another common way to say no matter how quiet it may be.

Your original sentence is natural and concise, especially in a descriptive or literary style.