Мне жалко, что ты всё ещё кашляешь: лучше бы ты сегодня остался дома.

Because жалко is used impersonally here. Russian often expresses feelings like this with:

• мне жалко = I feel sorry / I’m sorry
• literally: to me, it is pitiable/sad

So мне is in the dative case and marks the person experiencing the feeling.

Compare:

• Мне жалко тебя. = I feel sorry for you.
• Мне жалко, что ты кашляешь. = I’m sorry that you’re coughing.

You would not say я жалко here.

Almost. In this sentence, they are basically interchangeable:

• Мне жалко, что ты всё ещё кашляешь.
• Мне жаль, что ты всё ещё кашляешь.

Both mean I’m sorry that you’re still coughing.

The main difference is tone:

• жаль is a bit more neutral or standard
• жалко is a bit more conversational and emotionally warm

Also, жалко can often mean reluctant to give up / sorry to waste, for example:

• Мне жалко денег. = I hate to spend the money / I feel sorry for the money.

But in your sentence, it simply expresses sympathy.

Here что means that and introduces a clause:

• Мне жалко, что ты всё ещё кашляешь.
• I’m sorry that you’re still coughing.

So the structure is:

• мне жалко = I’m sorry
• что ты всё ещё кашляешь = that you’re still coughing

This is a very common pattern in Russian:

• Жаль, что ты не пришёл. = It’s a pity that you didn’t come.
• Хорошо, что ты позвонил. = It’s good that you called.

Всё ещё means still and emphasizes that the situation continues.

• ещё on its own can mean still, yet, more, or another, depending on context
• всё ещё is more clearly still

So:

• ты ещё кашляешь = you’re still coughing
• ты всё ещё кашляешь = you’re still coughing; the continuation is a bit more explicit/emphatic

English learners often find всё ещё useful because it maps neatly onto still.

Кашляешь is:

• 2nd person singular
• present tense
• from the imperfective verb кашлять = to cough

So it means:

• you are coughing
• or in context, you’re still coughing

The imperfective aspect is natural here because coughing is viewed as an ongoing process or repeated action, not as one completed event.

Compare:

• Ты кашляешь. = You’re coughing / You cough.
• Ты всё ещё кашляешь. = You’re still coughing.

There is no perfective verb here because the speaker is talking about a continuing symptom.

Лучше бы is a very common expression meaning something like:

• it would be better if...
• you’d better have...
• sometimes you really should have...

In your sentence:

• лучше бы ты сегодня остался дома

This means roughly:

• it would have been better if you had stayed home today
• or more naturally in English: you really should have stayed home today

This construction often expresses:

• advice
• regret
• mild criticism
• hindsight

It is very common in spoken Russian.

Examples:

• Лучше бы ты мне позвонил. = You should have called me.
• Лучше бы мы поехали поездом. = We should have gone by train.

Because the Russian conditional/subjunctive is normally formed with:

• a past tense verb
• plus бы

So even when the meaning is not strictly past, Russian still uses the past-tense form.

Pattern:

• сделал бы
• пошёл бы
• остался бы

In your sentence:

• лучше бы ты сегодня остался дома

literally has a past-form verb, but the meaning is conditional/hypothetical: it would be better if you stayed / had stayed home today.

This is normal Russian grammar, not a literal past tense in the English sense.

Also note:

• остался is masculine
• if speaking to a woman, it would be осталась

Because остаться дома means to stay at home / remain at home, which fits the idea of advice not to go out.

• остаться дома = stay home
• быть дома = be at home

In this sentence, the speaker is saying the person should not have gone out, so остаться дома is the natural choice.

Compare:

• Тебе лучше было остаться дома. = You should have stayed home.
• Ты был дома. = You were at home.

The second one only states location; it doesn’t express the idea of staying instead of going somewhere else.

Because дома is a special adverb meaning at home.

So:

• дома = at home
• домой = homeward / to home
• в доме = in the house/building

In your sentence:

• остался дома = stayed home / stayed at home

Compare:

• Я дома. = I’m at home.
• Я иду домой. = I’m going home.
• Я в доме. = I’m in the house (focusing on the building itself)

English speakers often want to use в доме, but for the normal idea of at home, Russian usually uses дома.

It often sounds a bit stronger than plain advice. Depending on tone, лучше бы can suggest:

• concern
• regret
• mild reproach
• you should have known better

So this sentence can sound caring, but also slightly critical:

• I’m sorry you’re still coughing; you really should have stayed home today.

If you wanted softer, more neutral advice about the present, Russian might use:

• Тебе лучше сегодня остаться дома. = You’d better stay home today.

That sounds more like advice for now.
But лучше бы ты сегодня остался дома often sounds like the speaker thinks the person already made the wrong choice by not staying home.

The colon links the two parts closely: the second part explains the conclusion drawn from the first.

Structure:

• Мне жалко, что ты всё ещё кашляешь = statement of concern
• лучше бы ты сегодня остался дома = conclusion/recommendation based on that

So the colon works like:

• I’m sorry you’re still coughing: you should have stayed home today.

In English, you might also use a dash or even a full stop. In Russian, the colon is natural when the second clause explains or follows from the first.

Yes, Russian can often omit subject pronouns because the verb ending already shows the person:

• Мне жалко, что всё ещё кашляешь...
• Лучше бы сегодня остался дома.

That is grammatically possible in the right context.

But keeping ты makes the sentence more direct and personal. It can add:

• emphasis
• emotional involvement
• a sense of addressing the person clearly

So in this sentence, repeating ты sounds natural because the speaker is directly talking to someone with concern.

Yes. Russian word order is flexible, and changing it changes emphasis more than basic meaning.

For example:

• Лучше бы ты сегодня остался дома.
• Лучше бы сегодня ты остался дома.
• Ты бы лучше сегодня остался дома.

All are possible, but they highlight slightly different things.

The version in your sentence is very natural and neutral. It puts the focus on the recommendation as a whole. The word сегодня sits in the middle naturally and means today without special dramatic emphasis.