Стоит дочке открыть альбом, как она сразу начинает рисовать.

This is a set construction meaning as soon as ..., the moment ..., or no sooner ... than ....

So:

Стоит дочке открыть альбом, как она сразу начинает рисовать.

means roughly:

As soon as the daughter opens the album, she immediately starts drawing.

Literally, стоит usually means stands or is worth, but in this pattern it has a special idiomatic meaning: it only takes... / one need only....

A very literal unpacking would be:

It only takes the daughter to open the album, and she immediately starts drawing.

That is why the sentence sounds more natural in English as as soon as...

Yes, normally стоить can mean to cost or to be worth, and стоять means to stand. But here you are seeing the fixed expression:

стоит кому-то что-то сделать, как...

This means:

• it only takes someone to do something for...
• as soon as someone does something...

So in this sentence, стоит is not about physical standing.

Examples:

• Стоит мне выйти из дома, как начинается дождь.
  As soon as I leave the house, it starts raining.

• Стоит ему позвонить, как все волнуются.
  As soon as he calls, everyone gets worried.

So this is a special idiomatic use you should learn as a whole pattern.

Because this construction uses the person in the dative:

стоит + someone in dative + infinitive

So:

• дочке = to the daughter / for the daughter
• открыть = to open

The structure is basically:

Стоит дочке открыть альбом...
It only takes for the daughter to open the album...

This dative marks the person who performs the action of the infinitive.

More examples:

• Стоит мне начать, как все замолкают.
  As soon as I begin, everyone goes quiet.

• Стоит ему увидеть собаку, как он улыбается.
  As soon as he sees a dog, he smiles.

So дочке is not an object of открыть; it is the person who does the opening.

It is an infinitive because the construction requires it:

стоит + dative + infinitive

So after стоит дочке you expect a verb in the infinitive.

It is perfective (открыть) because the sentence focuses on a single completed trigger: the moment the album gets opened, the next action begins.

So:

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

Here, the idea is:

once she opens it, not while she is opening it

That is why открыть fits naturally.

No, here как does not mean how.

In this construction, как works as a conjunction introducing the result or immediately following action:

Стоит X, как Y.

So the meaning is something like:

• as soon as X, Y
• no sooner does X happen than Y happens

In this sentence:

• Стоит дочке открыть альбом = As soon as the daughter opens the album
• как она сразу начинает рисовать = she immediately starts drawing

So как is part of the set pattern, not a question word here.

Because the sentence has two parts:

1. Стоит дочке открыть альбом
2. как она сразу начинает рисовать

The second clause is introduced by как, so Russian punctuation separates the two clauses with a comma.

This is standard for this pattern:

• Стоит мне сесть, как звонит телефон.
• Стоит ей улыбнуться, как все оживляются.

So the comma is not optional here.

Альбом is in the accusative singular, because it is the direct object of открыть:

• открыть что? → альбом

Since альбом is masculine and inanimate, its accusative singular looks exactly like the nominative singular:

• nominative: альбом
• accusative: альбом

So the form does not change, even though the case is accusative.

Both are possible, but they are slightly different in meaning.

начинает рисовать means:

• starts drawing
• it emphasizes the beginning of the action

So the sentence paints a vivid picture: the moment she opens the album, she gets going right away.

If you said:

Стоит дочке открыть альбом, как она сразу рисует,
that would sound less natural in this context.

A more natural alternative would be:

Стоит дочке открыть альбом, как она сразу принимается рисовать.
or
Как только дочка откроет альбом, она сразу рисует / начинает рисовать depending on the intended nuance.

So начинает рисовать is chosen because it matches the idea of an immediate reaction.

Дочка is a common, affectionate, everyday word for daughter.

Compare:

• дочь — more neutral, dictionary/basic form
• дочка — warmer, more colloquial, often affectionate

In the sentence, дочке is the dative singular of дочка.

So this choice gives the sentence a slightly more personal, family-like tone.

Usually it suggests a repeated pattern or a typical reaction.

So the sense is:

Whenever she opens the album, she immediately starts drawing.

That habitual meaning comes from the whole construction and from the present tense начинает.

Even though открыть is perfective, the sentence is not necessarily about one single occasion. In these kinds of patterns, perfective can still describe the trigger event in a repeated situation.

Yes. A very common simpler version would be:

Как только дочка открывает / откроет альбом, она сразу начинает рисовать.

Depending on nuance:

• Как только дочка открывает альбом... = Whenever she opens the album...
• Как только дочка откроет альбом... = As soon as she opens the album...

The original version with Стоит ..., как ... is a bit more expressive and idiomatic. It strongly emphasizes how immediately the second action follows the first.