После дождя на улице мокро, поэтому я иду домой.

Because после always takes the genitive case.

• дождь = nominative, the dictionary form
• дождя = genitive singular

So:

• после дождя = after the rain / after rain

This is a very common pattern in Russian:

• после урока = after the lesson
• после работы = after work
• после фильма = after the film

So the form дождя is required by the preposition после.

It can mean either, depending on context. Russian has no articles like a or the, so дождя does not itself tell you whether it is the rain or just rain in a general sense.

In this sentence, English would usually translate it naturally as After the rain or After it rains, depending on context.

So the Russian phrase is normal and does not need an article.

Because Russian normally says на улице for outside / in the street / outdoors.

Literally, улица means street, but the expression на улице often functions more broadly as outside.

So:

• на улице холодно = it’s cold outside
• на улице темно = it’s dark outside
• на улице мокро = it’s wet outside

Using в улице would be incorrect here. With улица, Russian idiomatically uses на in this meaning.

Because in the present tense, Russian usually omits the verb “to be”.

So where English says:

• It is wet outside

Russian simply says:

• На улице мокро

There is no present-tense есть here. That is normal.

Compare:

• Я дома = I am at home
• Он врач = He is a doctor
• Сегодня тепло = It is warm today

If you wanted past or future, a form of быть would appear:

• На улице было мокро = It was wet outside
• На улице будет мокро = It will be wet outside

Here мокро is not an adjective agreeing with a noun. It is a predicative adverb / category-of-state word, used to describe a general condition.

So:

• улица мокрая = the street is wet
  
  • мокрая is an adjective describing улица
• на улице мокро = it is wet outside
  
  • мокро describes the situation or environment

This is a very common Russian pattern:

• холодно = cold
• тепло = warm
• темно = dark
• тихо = quiet

So мокро here means something like it is wet rather than wet attached to a specific noun.

Because поэтому means therefore / so / that’s why, and here it connects two parts of the sentence:

• После дождя на улице мокро
• поэтому я иду домой

In Russian, this kind of connection is normally separated by a comma.

So the comma marks the result relationship:

• It’s wet outside after the rain, so I’m going home.

Поэтому means therefore, so, for that reason, or that’s why.

It introduces a consequence:

• Идёт дождь, поэтому мы сидим дома.
  It’s raining, so we’re staying home.

In your sentence:

• После дождя на улице мокро, поэтому я иду домой.
  After the rain it’s wet outside, so I’m going home.

A useful point: поэтому is not the same as потому что.

• поэтому = therefore / so
• потому что = because

Compare:

• На улице мокро, поэтому я иду домой.
  It’s wet outside, so I’m going home.
• Я иду домой, потому что на улице мокро.
  I’m going home because it’s wet outside.

Because идти means to go in one direction, right now or as a specific trip, while ходить usually means to go habitually, repeatedly, or in various directions.

So:

• я иду домой = I am going home / I’m on my way home
• я хожу домой пешком = I go home on foot / I usually walk home

In this sentence, the speaker is talking about a specific action caused by the wet conditions, so иду is the natural choice.

Because домой is the normal Russian word for homeward / to home / home when talking about going to one’s home.

So:

• я иду домой = I’m going home

This is the standard expression.

Compare:

• дом = house/home
• дома = at home
• домой = homeward, to home

The alternatives mean different things:

• в дом = into a house/building
• к дому = toward the house, up to the house

So if you mean going home, use домой.

In modern Russian, домой is best understood as an adverb meaning homeward / home.

Learners often want to treat it like a regular case form of дом, but synchronically it functions as a fixed word:

• идти домой = go home
• ехать домой = drive/go home
• вернуться домой = return home

So it is better to memorize:

• дома = at home
• домой = home, to home

as a useful pair.

Yes, often it could be omitted if the context already makes the subject clear.

Russian frequently drops subject pronouns when they are understood:

• ...поэтому иду домой.

This can sound perfectly natural in conversation.

However, including я is also completely correct. It may sound slightly clearer, more explicit, or more neutral for learners and written examples.

So both are possible:

• ...поэтому я иду домой
• ...поэтому иду домой

Yes. Russian word order is fairly flexible, although different orders can slightly change emphasis.

The original sentence is neutral and natural:

• После дождя на улице мокро, поэтому я иду домой.

You could also say:

• На улице мокро после дождя, поэтому я иду домой.
• Поэтому я иду домой: после дождя на улице мокро.

These versions are grammatically possible, but the original sounds like a straightforward, standard way to say it.

So the main idea is:

• Russian word order is flexible
• but the given order is natural and easy to understand

Yes, but the meaning shifts slightly.

• После дождя на улице мокро = After the rain, it’s wet outside.
  This describes the general outdoor situation.
• После дождя улица мокрая = After the rain, the street is wet.
  This focuses on the street as a noun.

So both are correct, but they are not identical.

Use мокро when you want the general environmental condition, and мокрая when you want to describe a specific noun like улица.

Because in Russian, the present tense often expresses an action that is happening right now or is immediately underway.

So:

• я иду домой can mean I’m going home now or I’m heading home

It does not have to mean a general habit. It often describes a current, real movement.

If you wanted to emphasize a future one-time action more strongly, you might use пойду in some contexts:

• ...поэтому я пойду домой = ...so I’ll go home

But я иду домой is perfectly natural if the speaker is already setting off or is in the process of going.