Стоит мне открыть дверь, как дочка сразу спрашивает, где её альбом.

This is an idiomatic pattern meaning as soon as I open the door..., the moment I open the door..., or no sooner do I open the door than....

The idea is that one action happens immediately after another. Here, the speaker means that the daughter asks her question right away whenever the speaker opens the door.

By itself, стоить often does mean to cost, and стоять means to stand. But in this sentence, стоит is part of a fixed construction:

стоит кому-то + infinitive, как...

This means it only takes someone to do X for Y to happen.

So:

Стоит мне открыть дверь, как дочка сразу спрашивает...
= As soon as I open the door, my daughter immediately asks...

This is a common literary or slightly elevated way to show an immediate consequence.

Because this construction requires the person in the dative:

стоит мне открыть...
стоит ему сказать...
стоит нам выйти...

So мне here means something like for me:

it only takes for me to open the door...

This is normal grammar for this pattern; you do not use я here.

It is an infinitive because the construction is:

стоит + dative + infinitive

So after стоит мне, you expect an infinitive.

It is perfective because открыть presents the action as a single completed event: the door gets opened, and that triggers the next action.

That fits the meaning very well:

• открыть = to open, as a completed act
• открывать = to be opening / to open habitually or repeatedly

In this sentence, the important point is the moment the door is opened, so открыть is the natural choice.

No. Here как is not the question word how.

In this pattern, как introduces the result or next event:

Стоит мне открыть дверь, как дочка сразу спрашивает...

So here как is part of the structure and means something like:

• and then
• when
• than in no sooner... than...

You should learn стоит..., как... as one linked pattern.

The present tense here shows a habitual or repeated action.

The sentence does not describe just one specific occasion. It describes what normally happens:

Whenever I open the door, my daughter immediately asks...

That is why Russian uses спрашивает.

If you wanted one specific past event, you would use a past form, for example:

Стоило мне открыть дверь, как дочка сразу спросила...

Yes. A very common neutral alternative is:

Как только я открываю дверь, дочка сразу спрашивает, где её альбом.

That also means As soon as I open the door, my daughter immediately asks where her album is.

The difference is mostly stylistic:

• Стоит мне открыть дверь, как... = more expressive, sometimes more literary
• Как только... = very common and neutral

Дочка is an everyday, affectionate form of дочь.

• дочь = daughter, more neutral or formal
• дочка = daughter, but warmer, more personal, often used in normal family speech

So дочка sounds natural and affectionate here.

Because свой normally refers back to the subject of its own clause.

In the embedded clause где её альбом, the daughter is not functioning as the grammatical subject of that clause. So Russian naturally uses её.

That is why:

дочка спрашивает, где её альбом
is natural.

Using свой here would sound odd to most speakers.

Because Russian usually omits есть in present-tense sentences of this kind.

So:

где её альбом
literally looks like where her album, but it means
where her album is

This is completely normal Russian. The verb to be is often omitted in the present tense.

Сразу means immediately, right away, or at once.

It emphasizes how quickly the daughter reacts after the door is opened.

So the sentence is not just saying she asks; it says she asks without delay.

Because the sentence has two clauses:

• Стоит мне открыть дверь
• как дочка сразу спрашивает, где её альбом

In Russian, these are separated by a comma. With the pattern стоит..., как..., the comma is standard.