Едва я открыл папку «Входящие», как увидел важное письмо от начальницы.

It is a fixed pattern meaning hardly had ... when ... or no sooner ... than .... It emphasizes that the second action happened immediately after the first one.

So the sentence has a stronger sense of immediacy than a plain when.

No. In this sentence, как is not the question word how. It is part of the conjunction pattern едва ..., как ....

Here it works more like when or than in English patterns such as hardly had I opened it, when... or no sooner had I opened it than....

Not always. Едва has two common uses:

1. As an adverb: barely

   • Я едва успел. = I barely made it.

2. As a conjunction at the start of a clause: hardly had / as soon as

   • Едва я вошёл, как он заговорил. = Hardly had I come in when he started talking.

In your sentence, it is the second use.

Because the sentence describes two completed actions in sequence:

• открыл = opened
• увидел = saw

The perfective aspect is natural here because:

• the folder was opened once, as a completed action
• the important email was then noticed as a single event

If you used imperfective forms, the sentence would sound more like an ongoing process, repetition, or background action, which is not the point here.

Открыть is perfective, and открыл means opened as a completed act. That fits the meaning here: he opened the folder, and right after that he saw the email.

Открывал would be imperfective and would suggest something like:

• he was in the process of opening it
• he used to open it
• the action is being described without focus on completion

That does not match this sentence well.

In the Russian past tense, singular verbs agree with the subject in gender.

So:

• я открыл = I opened, said by a male speaker
• я открыла = I opened, said by a female speaker

The same applies to увидел / увидела.

This sentence therefore suggests that the speaker is male.

Because папка is the direct object of открыл.

The noun папка is feminine, and its accusative singular form is папку:

• nominative: папка
• accusative: папку

So открыл папку literally means opened the folder.

Yes. Папка is used for both:

• a physical folder
• a digital folder on a computer or in an email program

In this sentence, because of Входящие, it clearly means a mail folder, basically the inbox folder.

Входящие is the usual Russian label for Inbox.

Literally, it comes from the idea of incoming messages or emails. It is plural because it originally relates to something like:

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

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

Because here Входящие is the name of the folder, written as a title: папку «Входящие».

In Russian, titles and names placed after a general noun often stay in their base form, especially when written in quotes:

• папка «Входящие»
• в папке «Входящие»
• из папки «Входящие»

The generic noun changes, but the title usually stays the same.

Because важное agrees with письмо.

Письмо is:

• neuter
• singular
• here in the accusative as the direct object of увидел

For an inanimate neuter noun, the accusative form looks the same as the nominative, so:

• важное письмо

The adjective and noun match in gender, number, and case.

Because от means from, and when it marks the source or sender, it takes the genitive case.

So:

• начальница = female boss
• от начальницы = from the female boss

That is why the ending changes to -ы.

Because начальница means a female boss, while начальник means a male boss.

So:

• от начальника = from the male boss
• от начальницы = from the female boss

This sentence tells you the boss is female.

Russian often leaves out the subject when it is already clear from context.

Here the subject of both verbs is the same person, so after Едва я открыл..., the second я is easy to understand without repeating it:

• Едва я открыл..., как увидел...

You could say как я увидел..., but it would be less natural here unless you wanted extra emphasis.

Because this is a complex sentence with two clauses:

• Едва я открыл папку «Входящие»
• как увидел важное письмо от начальницы

In Russian, clauses in this kind of structure are separated by a comma. With the pattern едва ..., как ..., the comma is required.

Yes. Как только я открыл папку «Входящие», я увидел... is perfectly natural.

The difference is mainly in nuance:

• едва ..., как ... sounds a bit more emphatic and sometimes slightly more literary
• как только ... is very common and neutral

Both express that the second action happened immediately after the first.