Один винт выпал из стула, и стул начал шататься.

It is literally the number one, but in sentences like this it often does some of the work that English a does.

So Один винт выпал... can mean:

• One screw fell out...
• or more naturally in context, A screw fell out...

Russian has no articles, so words like один, какой-то, or just bare nouns can help express that idea in different ways.

Here, один винт suggests:

• a single screw
• one of the screws, not all of them
• new information being introduced into the story

Without один, Винт выпал из стула would still be grammatical, but it would sound a bit less specific.

Possibly, depending on what kind of fastener you mean.

Very roughly:

• винт = screw, often a machine screw
• шуруп = screw that goes into wood or similar material
• болт = bolt

In everyday speech, people are not always technically precise, so some overlap happens. In a chair, шуруп might be very realistic if it is screwed into wood, but винт is also understandable and common enough in non-technical speech.

So for a learner:

• винт is perfectly normal here
• but in real life, the exact word may depend on the chair construction

Because выпал means fell out, while упал means just fell down.

Compare:

• упасть = to fall
• выпасть = to fall out, to come out by falling

Here the idea is not just that the screw fell somewhere. The important point is that it came out of the chair. That is why выпал is the better verb.

So:

• винт упал = the screw fell
• винт выпал из стула = the screw fell out of the chair

Стула is genitive singular.

That happens because the preposition из requires the genitive case when it means out of / from inside.

So:

• стул = nominative
• из стула = out of the chair

A few similar examples:

• из дома = out of the house
• из коробки = out of the box
• из сумки = out of the bag

So the form is not random. It is there because из controls the genitive.

Yes, and that is also very natural.

There is a small difference in perspective:

• Один винт выпал из стула focuses on the screw coming out of the chair
• У стула выпал один винт focuses more on the chair as the object that has lost a screw

Both are understandable and natural. In everyday Russian, у стула выпал винт is very common because Russian often uses у to talk about something belonging to or associated with something.

So both work, but they frame the situation a little differently.

Because repeating the noun avoids ambiguity.

If you said:

• Один винт выпал из стула, и он начал шататься

then он could in theory refer to:

• the screw
• or the chair

Even though logic tells us the chair is wobbling, Russian often repeats the noun to keep the sentence clear.

So:

• ..., и стул начал шататься = very clear
• ..., и он начал шататься = grammatically possible, but less clear

This is very common in Russian. Repetition is often more acceptable than in English.

Начал шататься means began to wobble.

It emphasizes the start of the action:

• first the screw fell out
• then the chair started wobbling

If you used шатался, that would mean was wobbling / used to wobble, which describes the state itself, not its beginning.

Compare:

• стул начал шататься = the chair started to wobble
• стул шатался = the chair was wobbling

So начал + infinitive is a very common way to show the beginning of an action.

Here шататься means something like:

• to wobble
• to rock
• to be unsteady
• to sway loosely

The -ся form matters.

Compare:

• шатать = to shake something
• шататься = to shake/wobble, to be wobbling

So:

• Я шатаю стул = I am shaking the chair
• Стул шатается = the chair is wobbling

In this sentence, the chair is not shaking something else. It itself has become unstable, so шататься is the correct form.

Because in Russian past tense, the verb agrees with the subject in gender and number.

Here:

• винт is masculine singular, so выпал
• стул is masculine singular, so начал

Compare:

• masculine: выпал, начал
• feminine: выпала, начала
• neuter: выпало, начало
• plural: выпали, начали

Examples:

• Гайка выпала = the nut fell out
• Кресло начало шататься = the armchair began to wobble
• Ножки начали шататься = the legs began to wobble

Because after начал Russian normally uses the infinitive that names the action itself, and here the action is an ongoing process: wobbling.

Шататься is imperfective because it describes the activity/state rather than a completed result.

The structure is:

• начать + imperfective infinitive

Examples:

• начал читать = began to read
• начала плакать = began to cry
• начали работать = began to work

So начал шататься is exactly what you would expect.

No, Russian word order is flexible, though different orders change the emphasis.

The original sentence:

• Один винт выпал из стула, и стул начал шататься.

This is a neutral, natural order.

Other possible versions:

• Из стула выпал один винт, и стул начал шататься.
• Стул начал шататься, потому что из него выпал один винт.

The basic meaning stays similar, but the focus shifts:

• starting with один винт highlights the screw
• starting with из стула highlights where it came from
• starting with стул highlights the chair and its condition

So the original is not the only possible order, but it is a very normal one.

Because и here connects two separate clauses, each with its own subject and verb:

• Один винт выпал из стула
• стул начал шататься

In Russian, when и links two independent clauses, a comma is usually needed.

So the comma is there for the same basic reason as in English:

• one full clause
• then another full clause joined by and

If и connects only words inside one clause, then there is usually no comma:

• винт и гайка
• сел и начал читать

But here it joins two full statements, so the comma is correct.

It describes a single event in the past.

That is shown mainly by:

• выпал: perfective past, a completed event
• начал: also a completed past event meaning began
• шататься: the action that started as a result

So the sequence is:

1. a screw came out
2. as a result, the chair started wobbling

If you wanted a habitual meaning, Russian would look different, for example with repeated context words or different aspect choices.

So this sentence sounds like one specific incident, not something that happened regularly.