У порога стоит старый стул, а за калиткой начинается тихий двор.

У means by, near, at, and it normally requires the genitive case.

So:

• порог = threshold, doorstep
• у порога = by the threshold / at the doorstep

That is why порог changes to порога.

This is a very common pattern:

• у дома = by the house
• у двери = by the door
• у окна = by the window

So у порога стоит старый стул literally has the structure By the threshold stands an old chair.

Because за can take different cases depending on the meaning.

• за + instrumental = location, behind/beyond
• за + accusative = motion, to behind / going beyond

Here there is no movement behind the gate. It describes where something begins from the speaker’s point of view: behind/beyond the gate. So Russian uses the instrumental:

• калитка → калиткой

Compare:

• за калиткой начинается тихий двор = beyond the gate, a quiet yard begins
• идти за калитку = to go beyond the gate

So за калиткой is a location phrase.

Калитка is usually a small gate, especially one in a fence around a house, garden, or yard.

It is not the main large gate for vehicles; it is more like a little pedestrian gate.

So:

• ворота = large gate
• калитка = small gate

That helps create a very specific image in the sentence: a threshold, then a little gate, then a yard beyond it.

In Russian, verbs like стоять, лежать, and висеть are often used where English would simply say there is.

Russian likes to describe the position of an object:

• стоит = stands
• лежит = lies
• висит = hangs

A chair is thought of as something that typically stands, so:

• У порога стоит старый стул = By the threshold stands an old chair

Using есть here would sound unnatural. Russian usually avoids есть in simple present-tense existence sentences of this kind.

Both are possible, but they feel slightly different.

• Старый стул стоит у порога = more neutral; first mentions the chair
• У порога стоит старый стул = first sets the scene, then introduces the chair

Russian word order is flexible, and putting the location first often makes the sentence more descriptive or literary. It is very common when introducing something in a place:

• На столе лежит книга
• У окна сидит девочка
• В саду растёт яблоня

So here the sentence paints the setting first: At the threshold...

Yes. In Russian, начинаться can be used with places, areas, roads, forests, fields, and similar spaces.

So за калиткой начинается тихий двор means something like:

• beyond the gate, a quiet yard begins
• past the gate, the quiet yard starts

This sounds more spatial and descriptive than simply saying there is a quiet yard. It suggests that once you pass the gate, you enter that yarded space.

It is a natural Russian way to describe a landscape or scene.

Двор is in the nominative singular because it is the subject of начинается.

The basic structure is:

• тихий двор начинается = a quiet yard begins

The phrase за калиткой is just the location.

So the grammar is:

• за калиткой = location phrase
• начинается = verb
• тихий двор = subject

Even though the English translation may sound unusual if translated word-for-word, the Russian grammar is straightforward.

А often connects two parts of a sentence by shifting the viewpoint or making a mild contrast.

Here it does not mean a strong but. It is more like:

• and meanwhile
• while
• and as for
• whereas in a light descriptive sense

So the sentence moves from one image to another:

• У порога стоит старый стул, а за калиткой начинается тихий двор.

This feels like:

• By the threshold stands an old chair, and beyond the gate a quiet yard begins.

If you used и, the link would feel more like simple addition.
If you used но, it would sound like a stronger contrast, which is not really the point here.

Because both adjectives agree with the nouns they describe in gender, number, and case.

• стул is masculine singular nominative → старый стул
• двор is masculine singular nominative → тихий двор

So:

• старый matches стул
• тихий matches двор

This is basic adjective agreement in Russian.

Usually quiet yard is the best translation.

Тихий can mean:

• quiet
• peaceful
• calm
• still

It does not always mean complete silence. In this sentence, it probably suggests a peaceful, calm courtyard or yard, not necessarily one with absolutely no sound.

So тихий двор gives a gentle, atmospheric image.

Yes:

• У = by, near; preposition requiring the genitive
• порога = genitive singular of порог; threshold / doorstep
• стоит = stands; 3rd person singular of стоять
• старый = old; masculine singular nominative

• стул = chair; masculine singular nominative

• а = and / while / whereas; a linking word with a slight contrast or shift
• за = behind / beyond
• калиткой = instrumental singular of калитка; small gate
• начинается = begins; 3rd person singular of начинаться
• тихий = quiet; masculine singular nominative
• двор = yard / courtyard; masculine singular nominative

So the sentence is built from two descriptive clauses:

1. У порога стоит старый стул
2. а за калиткой начинается тихий двор