Когда почтальон долго не приходит, я сама иду к почтовому ящику и проверяю, нет ли там письма.

Because this sentence describes a repeated or habitual situation, not one single future event.

• приходит is the imperfective present
• In Russian, the imperfective present can be used for things that happen regularly, typically, or in a general situation

So Когда почтальон долго не приходит... means something like:

• When the mail carrier hasn’t been coming for a long time
• When the mail carrier takes a long time to come
• When the mail carrier is late

If you said Когда почтальон долго не придёт, that would point more toward a single future occasion, and it would sound unnatural here.

Literally, it is something like does not come for a long time.

In Russian, долго often combines with negation like this:

• Он долго не звонил = He didn’t call for a long time
• Автобус долго не приходил = The bus didn’t come for a long time

So почтальон долго не приходит does not mean he comes slowly. It means there is a long delay before he comes, or he hasn’t shown up for quite a while.

сама adds emphasis: I myself, I personally, I go on my own.

Without сама:

• я иду к почтовому ящику = I go to the mailbox

With сама:

• я сама иду к почтовому ящику = I myself go to the mailbox

It suggests something like:

• I don’t wait for someone else
• I personally take action
• I go and check myself

Since the speaker is female, the form is сама. A male speaker would say сам.

After the preposition к meaning to / toward, Russian uses the dative case.

The base form is:

• почтовый ящик = mailbox

After к, it becomes:

• к почтовому ящику

Case breakdown:

• почтовый → почтовому
• ящик → ящику

So:

• иду к почтовому ящику = I’m going to the mailbox

Because иду means I am going / I go in one specific instance or direction, while хожу usually means I go regularly / I walk around / I am in the habit of going.

Here the speaker means a specific action in response to the delay:

• я сама иду к почтовому ящику = I go to the mailbox myself

If you said я сама хожу к почтовому ящику, it would sound more like a habit:

• I myself go to the mailbox regularly

So иду fits better.

Because Когда почтальон долго не приходит is a subordinate clause introduced by когда.

Russian separates subordinate clauses with commas:

• Когда X, Y
• If X, Y
• Because X, Y

So the structure is:

• Когда почтальон долго не приходит,
  я сама иду к почтовому ящику...

This comma is required.

Because the main clause contains two coordinated actions:

1. я сама иду к почтовому ящику
2. (я) проверяю, нет ли там письма

So и simply means and:

• I go to the mailbox and check...

Russian often omits the repeated subject я in the second part because it is already understood.

ли is a particle used to form an indirect yes/no question.

The phrase проверяю, нет ли там письма literally means:

• I check whether there is no letter there
• more naturally: I check whether there is a letter there

This pattern is very common in Russian:

• Спроси, дома ли он. = Ask whether he is home.
• Посмотри, не пришёл ли автобус. = See whether the bus has arrived.
• Проверь, нет ли ошибки. = Check whether there is an error.

So ли often corresponds to English whether.

In Russian, ли usually comes after the word it focuses on.

Here the key word is нет:

• нет ли там письма

This is the normal order for this structure. Russian does not place ли at the beginning the way English uses whether.

Compare:

• Я не знаю, придёт ли он. = I don’t know whether he’ll come.
• Проверь, дома ли мама. = Check whether Mom is home.
• Спроси, есть ли хлеб. = Ask whether there is bread.

Because after нет, Russian uses the genitive case.

Base form:

• письмо = letter

After нет:

• нет письма = there is no letter

So in нет ли там письма, письма is genitive singular.

This is a very important pattern:

• есть письмо = there is a letter
• нет письма = there is no letter

Both are grammatically possible, but нет ли is very natural in Russian when someone is checking for the possible presence of something.

It often implies:

• to see if there isn’t any...
• to see whether maybe there is...

Russian frequently uses нет ли in this kind of checking context:

• Проверь, нет ли новых сообщений.
• Посмотри, нет ли ключей на столе.

English would usually phrase this positively:

• Check if there is a letter there

But Russian often prefers the negative-style construction.

там means there.

In this sentence it refers to the mailbox: the speaker goes to the mailbox and checks whether there is a letter there, i.e. in it / there in the mailbox.

Russian often uses там where English might use:

• there
• in it
• inside

So нет ли там письма is completely natural.

Yes. Russian word order is flexible, though each version has a slightly different emphasis.

For example:

• Когда почтальон долго не приходит, я сама иду к почтовому ящику и проверяю, нет ли там письма.
  Neutral, natural order.

Possible alternatives:

• Я сама иду к почтовому ящику, когда почтальон долго не приходит...
  More emphasis on what I do

• ...и проверяю, письма ли там нет
  This would sound unnatural; you cannot move things freely in every case.

So Russian word order is flexible, but not random. The original sentence sounds very standard and natural.

Russian has no articles.

So nouns like:

• почтальон
• почтовому ящику
• письма

can mean:

• the mail carrier / a mail carrier
• the mailbox / a mailbox
• the letter / a letter

The exact meaning is understood from context. In this sentence, English naturally uses the mail carrier and the mailbox, but Russian does not need separate words for that.

Почтальон is a normal, understandable word meaning mail carrier / postman / postal worker.

Depending on context, modern Russian may also use more official or neutral expressions, but почтальон is still common and perfectly natural in everyday language, especially in ordinary descriptive sentences like this one.

The pattern is:

• verb of checking/asking/seeing/thinking + indirect question

Here:

• проверяю = I check
• нет ли там письма = whether there is a letter there

This kind of structure is extremely useful in Russian. Similar examples:

• Смотрю, пришёл ли он. = I’m checking whether he came.
• Спрошу, свободен ли он. = I’ll ask whether he is free.
• Проверю, есть ли вода. = I’ll check whether there is water.

So this sentence is a good example of how Russian introduces embedded yes/no questions.