Папа собирает новый шкаф, пока мама готовит ужин.

Папа is the everyday, family-style word for dad. A more formal or neutral word would be отец.

So:

• папа = dad
• отец = father

In this sentence, папа and мама match in tone and sound natural for ordinary speech.

Yes, собирать / собрать can mean to collect, but in this context собирает шкаф means is assembling / is putting together a wardrobe/cabinet.

That is a very common use with furniture:

• собирать шкаф = assemble a wardrobe
• собирать стол = assemble a table
• собирать кровать = assemble a bed

So here собирает does not mean he is gathering wardrobes; it means he is putting one together.

Because шкаф is the direct object of собирает, so it is in the accusative case. But шкаф is masculine singular inanimate, and for masculine inanimate nouns, the accusative looks the same as the nominative.

So:

• nominative: новый шкаф
• accusative: новый шкаф

That is why nothing changes visibly here.

The adjective новый agrees with шкаф in:

• gender: masculine
• number: singular
• case: accusative

But since this is masculine inanimate, the form still looks like nominative.

Because ужин is the direct object of готовит.

• готовить что? = to prepare what?
• ужин = dinner

So Russian simply uses the accusative directly:

• готовит ужин = prepares dinner / is cooking dinner

No preposition is needed.

Here пока means while.

So the sentence means that the two actions happen at the same time:

• Dad is assembling a new wardrobe,
• while Mom is cooking dinner.

Be careful: пока can mean different things in other contexts, such as:

• while
• until
• even bye in conversation (Пока!)

But in this sentence, the meaning is clearly while.

Because пока мама готовит ужин is a subordinate clause.

Russian normally separates this kind of clause with a comma:

• Папа собирает новый шкаф, пока мама готовит ужин.

This is similar to English writing with while joining two clauses, although Russian is generally stricter about using the comma here.

Yes. In Russian, the present tense of an imperfective verb can often mean either:

• something happening right now, or
• something happening regularly / habitually

So this sentence could mean:

• Dad is assembling a new wardrobe while Mom is cooking dinner (right now)
• or, depending on context, a more general repeated situation

Here the most natural reading is the ongoing one: both actions are in progress at the same time.

Also notice that Russian does not have a separate form exactly like the English is assembling / is cooking. The simple present form often covers that meaning.

They are imperfective because the sentence describes actions as ongoing processes, not as completed results.

• собирает comes from собирать (imperfective)
• готовит comes from готовить (imperfective)

That fits the idea of two actions unfolding at the same time.

If you used perfective future forms instead, the meaning would change. For example, perfective verbs would focus more on completion, not the ongoing scene.

Yes. Russian word order is flexible, because case endings show the grammatical roles.

For example, you could also say:

• Пока мама готовит ужин, папа собирает новый шкаф.

This means the same thing: While Mom is cooking dinner, Dad is assembling a new wardrobe.

The difference is mainly in emphasis:

• starting with Папа... highlights Dad first
• starting with Пока мама... sets the time/background first

Because мама is the subject of готовит, so it is in the nominative case.

Even though мама refers to a female person, it belongs to the noun pattern that often ends in -а / -я. Its nominative singular form is simply:

• мама

If it were in another case, the ending would likely change. For example:

• nominative: мама
• accusative: маму
• genitive: мамы

But here it is the subject, so nominative is correct.

Шкаф is a general word for a tall cabinet, cupboard, or wardrobe, depending on context.

So новый шкаф could be translated as:

• a new wardrobe
• a new cabinet
• sometimes a new cupboard

In a sentence about assembling it, wardrobe or cabinet is often the most natural translation. The exact English word depends on what kind of furniture is meant.