Я открыла папку «Входящие» и увидела письмо от нового отправителя.

Because the speaker is female.

In the past tense, Russian verbs agree with the subject in gender and number:

• masculine: открыл, увидел
• feminine: открыла, увидела
• neuter: открыло, увидело
• plural: открыли, увидели

So Я открыла ... и увидела ... means I am a woman/girl.
If a man were speaking, it would be:

• Я открыл папку ... и увидел письмо ...

Yes, Russian often omits the subject pronoun when it is clear from the verb.

So this sentence could also be:

• Открыла папку Входящие и увидела письмо от нового отправителя.

That still means I opened the Inbox folder and saw a letter/email from a new sender, and the feminine verb endings still show that the speaker is female.

Including Я can make the sentence a little more explicit, contrastive, or simply clearer for learners.

Because папка is the direct object of открыла, so it goes into the accusative case.

• nominative: папка = folder
• accusative: папку = folder as the object of the action

Compare:

• Папка лежит на столе. = The folder is lying on the table.
• Я открыла папку. = I opened the folder.

Since папка is feminine and inanimate, its accusative singular ends in -у.

Because письмо is also a direct object, but it is a neuter inanimate noun, and for many neuter inanimate nouns, the accusative singular is the same as the nominative singular.

So:

• nominative: письмо
• accusative: письмо

That is why you get:

• увидела письмо = saw a letter/email

This is different from папка → папку, where the accusative changes visibly.

Because the preposition от requires the genitive case.

So:

• новый отправитель = a new sender (nominative)
• от нового отправителя = from a new sender (genitive)

Both words change:

• новый → нового
• отправитель → отправителя

This is very common in Russian:

• от друга = from a friend
• от сестры = from a sister
• от нового отправителя = from a new sender

The dictionary form is отправитель.

Here is the pair:

• отправитель = sender
• отправителя = of/from the sender

So in this sentence, отправителя is just the genitive singular form after от.

Входящие literally means something like incoming ones or incoming messages.

It comes from the adjective входящий = incoming. In interface language, Russian often uses this word by itself as a label for an inbox folder:

• Входящие = Inbox

It looks plural because historically it stands for something like:

• входящие письма = incoming letters/emails
• входящие сообщения = incoming messages

So even though English uses the singular-looking word Inbox, Russian commonly uses Входящие.

Because it is the name of a folder/interface label.

In Russian typography, the usual quotation marks are:

• « ... »

So:

• папку «Входящие» = the folder Inbox

These marks show that Входящие is being treated as a specific title or label, not just an ordinary adjective.

In less formal writing, especially in tech contexts, you may also see folder names without quotation marks.

They are perfective verbs:

• открыла ← открыть
• увидела ← увидеть

Perfective verbs present the actions as completed, whole events:

• she opened the folder
• she saw a message

That fits this sentence, because it describes two completed actions in sequence.

The imperfective counterparts would be:

• открывала ← открывать
• видела ← видеть

Those would sound more like ongoing, repeated, or background actions depending on context.

Because увидела means caught sight of / saw as a completed event.

Compare:

• видела = was seeing / saw (in a more general or ongoing sense)
• увидела = saw, noticed, caught sight of

In this sentence, the idea is that after opening the folder, she noticed a message there. That is why увидела works very naturally.

Yes. In a sentence like this, и simply means and, and the order of the verbs usually suggests the order of events:

1. opened the folder
2. saw the message

So Russian does not need a separate word like then here, though you could add one in another sentence if you wanted extra emphasis.

Because both verbs are perfective, the sequence feels especially clear and complete.

Yes, Russian word order is fairly flexible.

The neutral order here is:

• Я открыла папку «Входящие» и увидела письмо от нового отправителя.

But other orders are possible depending on emphasis, for example:

• Письмо от нового отправителя я увидела, открыв папку «Входящие».
• Я увидела письмо от нового отправителя, когда открыла папку «Входящие».

The original version is natural and straightforward, especially for a simple narrative statement.

It can mean either in a general sense, but in this context it most naturally means an email/message, because of папку «Входящие».

So even though письмо literally means letter, in modern Russian it is also commonly used for email.

Context tells you which meaning is intended.

Because Russian has no articles.

English distinguishes:

• a folder
• the folder

Russian usually does not mark that difference with a separate word. Instead, definiteness is understood from:

• context
• word order
• stress/emphasis
• the situation

So папку can mean a folder or the folder, depending on context. The same is true for письмо and нового отправителя.

Yes, it is natural if you want to refer to the folder explicitly.

• папка «Входящие» = the Inbox folder

But depending on context, Russians might also simply say:

• во Входящих = in Inbox
• открыла Входящие = opened Inbox

So the sentence is perfectly natural, but in everyday speech the noun папка may sometimes be omitted if it is obvious you are talking about an email folder.