Я кашлянула один раз и поняла, что мне лучше сегодня остаться дома.

Because in the past tense, Russian verbs agree with the subject in gender and number if the subject is singular.

Here the speaker is Я, and the form shows that the speaker is female:

• кашлянула = a woman coughed
• поняла = a woman understood/realized

Compare:

• masculine: я кашлянул, я понял
• feminine: я кашлянула, я поняла
• plural: мы кашлянули, мы поняли

So this sentence was said by a woman.

Кашлянула is a perfective verb form from кашлянуть, and it usually means to cough once or to give a cough.

By contrast:

• кашляла = was coughing / coughed repeatedly / coughed in general
• кашлянула = coughed once, a single completed cough

So Я кашлянула один раз gives the idea of one specific cough, not an ongoing coughing fit.

Good question. Один раз is not absolutely necessary, but it adds extra explicitness and emphasis.

So:

• Я кашлянула = I coughed once / I gave a cough
• Я кашлянула один раз = I coughed once, one single time

The phrase один раз makes the situation more vivid and removes any doubt. In natural speech, Russian often uses both the perfective verb and a phrase like this together.

Here и literally means and, but in context it can also carry the sense of and then.

The sequence is:

1. Я кашлянула один раз
2. и поняла...

So the idea is: one thing happened, and then as a result, she realized something.

Russian often uses simple и where English might choose:

• and
• and then
• so

All of those are close in feeling, depending on context.

Что introduces a clause explaining what she realized.

• поняла, что... = realized that...

This is very common after verbs like:

• знать, что... = to know that...
• думать, что... = to think that...
• понимать, что... = to understand that...
• видеть, что... = to see that...

So поняла, что мне лучше сегодня остаться дома means she realized that it would be better for her to stay home today.

Because Russian often uses an impersonal construction here.

Literally, мне лучше остаться дома is something like:

• to me, it is better to stay home

So мне is in the dative case, because it marks the person for whom something is better, easier, necessary, possible, and so on.

This pattern is very common:

• мне лучше уйти = I had better leave
• тебе лучше подождать = you had better wait
• ему лучше не спорить = he had better not argue

So even though English uses I, Russian uses мне.

Here лучше means something like:

• it would be better
• had better
• probably should

So мне лучше сегодня остаться дома means:

• it would be better for me to stay home today
• I’d better stay home today

It is not just a plain comparison like better than something else. In this structure, лучше + infinitive often gives advice, judgment, or a practical conclusion.

Остаться is perfective, while оставаться is imperfective.

With лучше + infinitive, Russian often chooses the perfective when talking about a single complete decision or action:

• лучше остаться дома = better to stay home
• лучше пойти сейчас = better to go now
• лучше позвонить позже = better to call later

Here the speaker is making one concrete decision about today, so остаться fits well.

If you used оставаться, it would sound more like focusing on the process or a general ongoing situation, which is less natural here.

Because дома means at home, while домой means to home / homeward.

Compare:

• остаться дома = stay at home
• идти домой = go home

The verb остаться means remain/stay, so it takes a place where you remain. That is why дома is correct.

So:

• дома = location
• домой = direction

Usually no, not in the normal everyday sense of stay home.

• дома means at home, in the ordinary personal sense
• в доме means in the house/building

So:

• остаться дома = stay home
• остаться в доме = remain in the house

The second version sounds more physical and literal, as if the building itself matters. In this sentence, the idiomatic choice is definitely дома.

Russian word order is fairly flexible, and this sentence uses a natural, neutral order.

• мне лучше сегодня остаться дома

This places сегодня near the decision and makes today part of what she has realized.

Other word orders are possible, with slightly different emphasis:

• Сегодня мне лучше остаться дома = Today, I’d better stay home
• Мне лучше остаться дома сегодня = similar meaning, with today placed later
• Мне сегодня лучше остаться дома = also natural

So the meaning stays the same, but the focus can shift a little depending on placement.

In this sentence, сегодня naturally means today, but in context it often feels like for today or for the rest of today.

So the sense is not just calendar-day information. It also suggests a practical decision limited to this day:

• today is not a good day to go out
• today it is better to stay home

That nuance comes from the whole sentence, not from сегодня alone.