Стоит нам включить музыку, как брат начинает петь вместе с нами и смеяться.

Here стоит кому-то + infinitive, как ... is an idiomatic pattern meaning as soon as someone does X, Y happens or no sooner ... than ....

So:

• Стоит нам включить музыку, как ... = As soon as we turn on the music, ...
• A closer English-style equivalent is No sooner do we turn on the music than ...

Even though стоить often means to cost, in this pattern you should learn the whole expression as a set phrase.

Because this construction uses the dative case for the person who performs the infinitive action.

• нам = dative of мы
• включить is an infinitive
• so нам включить музыку literally means something like for us to turn on the music

This is common in impersonal Russian constructions. The logical doer is present, but not in the nominative.

After стоит in this pattern, Russian uses an infinitive:

• стоит нам включить музыку
• not стоит нам включаем музыку

The structure is basically:

• стоит + dative + infinitive, как ...

So the infinitive is required by the construction itself.

Because включить is perfective, and that fits the meaning here.

The sentence focuses on the moment the action happens as a trigger:

• включить = to turn on, as a completed event
• включать = to be turning on / to turn on repeatedly or as a process

In this sentence, the important idea is the moment we turn the music on, and then the brother reacts immediately. That is why the perfective verb включить is natural here.

No. Here как is not the question word how.

In this sentence, как introduces the result that follows immediately after the first action. In English, it works like:

• as soon as
• when
• than in no sooner ... than ...

So:

• Стоит нам включить музыку, как брат начинает...
• As soon as we turn on the music, my brother starts...

Because музыка is the direct object of включить.

• включить что? → музыку

So Russian uses the accusative here, just as English uses a direct object in turn on the music.

Because начинать / начать is followed by an infinitive.

So:

• начинает петь = starts singing
• начинает смеяться = starts laughing

In this sentence, one finite verb, начинает, governs two infinitives:

• петь
• смеяться

So the meaning is that he starts doing both actions.

Нами is the instrumental form of мы.

That is because the expression вместе с requires the instrumental case:

• вместе с кем? → с нами

So:

• вместе с нами = together with us

This is something worth memorizing as a chunk: вместе с + instrumental.

Because the sentence describes a habitual or repeated situation.

It means that whenever this happens, the brother reacts in this way. Russian often uses the present tense for this kind of general repeated action:

• Стоит нам включить музыку, как брат начинает...
• As soon as we turn on the music, my brother starts...

If you wanted to describe one specific event in the past, you would normally shift everything into the past, for example:

• Стоило нам включить музыку, как брат начал петь...

Yes. A learner might find a version with как только easier:

• Как только мы включаем музыку, брат начинает петь вместе с нами и смеяться.

Or, if you want a single past event:

• Как только мы включили музыку, брат начал петь вместе с нами и смеяться.

The original sentence is natural and idiomatic, but как только is often easier to understand at first.

The given word order is natural, but Russian word order is fairly flexible.

The version

• Стоит нам включить музыку, как брат начинает петь вместе с нами и смеяться

sounds smooth and standard.

You may sometimes see punctuation or slight rearrangement, but the core pattern stays the same:

• Стоит нам включить музыку, как брат начинает...

What matters most is keeping the construction стоит + dative + infinitive, как ... intact.