Мне жалко, что ты промок под дождём.

Because this is an impersonal construction in Russian.

• мне is the dative case of я
• жалко is a predicative word meaning something like it is sad / I feel sorry / I feel bad

So Мне жалко literally works more like:

• To me, it is sad
• or I feel sorry

Russian often uses this kind of structure for feelings and states:

• Мне холодно = I am cold
• Мне грустно = I am sad
• Мне жалко = I feel sorry / I feel bad

So мне is exactly what Russian grammar expects here.

Here жалко means something like:

• I’m sorry
• I feel bad
• I feel sorry for you
• It’s a pity

In this sentence, it expresses sympathy because something unpleasant happened to the other person.

A close synonym is жаль:

• Мне жалко, что ты промок под дождём.
• Мне жаль, что ты промок под дождём.

Both are natural.
Very roughly:

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

Что introduces the clause explaining what the speaker feels sorry about.

So:

• Мне жалко = I’m sorry / I feel bad
• что ты промок под дождём = that you got soaked in the rain

Together:

• Мне жалко, что... = I’m sorry that...

In English, that is often optional, but in Russian что is normally kept in this kind of sentence.

Промок is the past tense masculine singular form of the verb промокнуть, which means:

• to get soaked
• to become wet through

So ты промок means:

• you got soaked
• you became soaked through

Because the subject is understood as masculine here, the form is промок.

Other past forms would be:

• ты промокла — if speaking to a woman
• вы промокли — plural or polite you
• он промок
• она промокла

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

Here the subject is ты, and the sentence is addressed to one person who is understood to be male, so:

• ты промок

If the speaker were talking to a female, it would be:

• Мне жалко, что ты промокла под дождём.

This is one of the important differences from English: Russian past tense often shows gender.

Промокнуть is a perfective verb, and промок shows a completed result:

• the person ended up soaked

That fits the situation well, because the speaker is reacting to a finished event.

If you want to emphasize the result you got soaked, perfective is natural.

The imperfective partner is промокать / мокнуть in various contexts, but here the result matters most, so промок is the expected choice.

Literally, под дождём is something like under the rain, but in natural English it usually means:

• in the rain
• out in the rain
• caught in the rain

Russian commonly uses под with weather conditions like this:

• стоять под дождём = to stand in the rain
• гулять под снегом is less common, but the same idea exists with precipitation expressions

So in this sentence:

• промок под дождём = got soaked in the rain

It does not mean the person was physically under a specific object called rain. It is just the normal Russian way to express exposure to rainfall.

Because after под in the meaning of under or beneath, Russian normally uses the instrumental case.

The noun is:

• дождь = rain

Instrumental singular:

• дождём

So:

• под дождём = under/in the rain

This is a very useful pattern:

• под столом = under the table
• под деревом = under the tree
• под дождём = in the rain / under the rain

Because the correct form is дождём, with stress on -ём.

In many printed texts, ё is often written as е, so you may also see:

• под дождем

But it is still pronounced dazh-DYOM, not dazh-dem.

For learners, it is helpful to remember the real pronunciation with ё, even if native texts sometimes omit the dots.

Yes, absolutely. That is very natural.

Both are good:

• Мне жалко, что ты промок под дождём.
• Мне жаль, что ты промок под дождём.

Very roughly:

• жаль = a little more neutral, standard
• жалко = a little more conversational, sympathetic

In everyday speech, both are common.

The given word order is the most neutral and natural:

• Мне жалко, что ты промок под дождём.

Russian word order is flexible, but changes usually affect emphasis.

For example:

• Мне жалко, что под дождём ты промок.
  This puts more attention on под дождём.

• Что ты промок под дождём, мне жалко.
  Grammatically possible, but much less natural in ordinary conversation.

So for a learner, the original order is the safest and most idiomatic one.

Not really. It sounds natural and sympathetic.

It suggests:

• the speaker feels bad for the other person
• the speaker is showing concern

If you want slightly different tones, Russian offers other options:

• Мне жаль, что ты промок под дождём. — a bit more neutral
• Сочувствую. — I sympathize
• Как жаль, что ты промок под дождём! — more emotional
• Жалко, что ты промок под дождём. — more casual, with мне omitted because it is understood

So the original sentence is a normal, kind way to react.