Как бы малышка ни капризничала вечером, мама всё равно поёт ей тихую колыбельную и долго укачивает её на руках.

This is a very common Russian concessive pattern. Как бы ... ни means something like:

• no matter how ...
• however much ...
• even if ...

So Как бы малышка ни капризничала вечером means No matter how much the little girl fusses in the evening.

It does not mean a literal question with how. Here как introduces a concessive idea, not a real question.

In this construction, ни usually stands close to the verb, while как бы comes earlier. So the pattern is really:

Как бы + subject/other words + ни + verb

That is why you get:

• Как бы малышка ни капризничала...

and not necessarily Как бы ни малышка...

This is normal. The important thing is the overall frame как бы ... ни.

Great question. In this kind of construction, Russian often uses the past-tense form + бы to express something hypothetical, indefinite, or concessive.

So капризничала here is not really functioning as a normal past tense like she fussed. In Как бы ... ни капризничала, it is part of a fixed grammatical pattern.

Why капризничала specifically?

• малышка is feminine singular
• so the verb form matches that: капризничала

Compare:

• Как бы он ни старался... — no matter how hard he tries
• Как бы она ни старалась... — no matter how hard she tries

So the feminine -ла ending agrees with малышка.

Because this is a special concessive pattern. In Russian, ни is often used in expressions meaning:

• no matter who
• no matter where
• no matter how
• whatever
• however

Examples:

• Кто бы ни пришёл... — whoever comes
• Где бы ни был... — wherever he may be
• Как бы ни старался... — no matter how hard he tries

So in your sentence, ни does not simply negate the verb the way не would. It helps create the meaning no matter how much.

Малышка is in the nominative case because it is the subject of the subordinate clause:

• малышка капризничала — the little girl was fussing / fussed

Even though the clause begins with Как бы, the subject is still малышка.

Вечером is the instrumental singular of вечер, and Russian often uses the instrumental to mean at a certain time:

• утром — in the morning
• днём — in the daytime
• вечером — in the evening
• ночью — at night

So вечером here means in the evening.

This is a standard time expression, not something special to this sentence.

Всё равно means:

• all the same
• anyway
• still
• regardless

In this sentence it emphasizes that the mother's action does not change, despite the baby's fussing:

• Как бы малышка ни капризничала..., мама всё равно поёт...
• No matter how much the little girl fusses..., the mother still sings...

So всё равно is the main signal in the second clause that says: the result stays the same.

Because петь кому-то means to sing to someone.

So:

• поёт ей = sings to her

Here ей is the dative singular form of она.

Very common pattern:

• читать ребёнку — to read to a child
• сказать ему — to tell him
• петь ей — to sing to her

Because колыбельную is the direct object of поёт:

• петь что? — to sing what?
• колыбельную

So it takes the accusative case.

And the adjective тихую agrees with колыбельную:

• feminine
• singular
• accusative

Dictionary forms are:

• тихая
• колыбельная

In the sentence they become:

• тихую
• колыбельную

Also, тихая колыбельная means a soft/quiet lullaby.

Because the sentence describes an action as ongoing, repeated, or characteristic, not as a single completed event.

• поёт from петь — imperfective
• укачивает from укачивать — imperfective

This fits the idea of what the mother does in that situation:

• she sings to her
• she rocks her for a long time

If you used perfective forms, the sentence would sound more like a single completed event, which is not the focus here.

Russian often includes object pronouns even when the referent is clear.

So:

• укачивает её = rocks her / lulls her

The pronoun helps make the sentence explicit and smooth, especially after another object phrase like ей тихую колыбельную.

Could it be omitted in some contexts? Sometimes yes, if the meaning is completely obvious. But here укачивает её is very natural.

Also note that this её is accusative, because it is the direct object.

Literally, на руках means on the arms/hands.

Idiomatic English translation:

• in her arms
• while holding her
• in her arms, rocking her

Russian uses руки in the plural here. The phrase носить/держать/укачивать на руках is very common and means holding someone in your arms rather than putting them in a crib or bed.

Grammatically, руках is the prepositional plural after на in a location-type meaning.

Because the first part is a subordinate concessive clause, and the second part is the main clause.

Structure:

• Как бы малышка ни капризничала вечером,
• мама всё равно поёт ей...

Russian normally separates this kind of subordinate clause with a comma.

To some extent, yes. Russian word order is flexible, but the current order is natural and expressive.

This version:

• Как бы малышка ни капризничала вечером, мама всё равно...

puts the concessive idea first, and then the main point:

• despite that, the mother still does this

That makes the contrast very clear.

You may also see similar variants in Russian, but this sentence is already perfectly natural and well-structured.