Learn Hardcore Russian: Что бы ни случилось днём, вечером мне всё равно хочется немного тишины. - No matter what happens during the day, in the evening I still feel like having a bit of silence.

Together: что бы ни случилось → whatever happens / no matter what happens.
It’s not a single fixed idiom, but a very common pattern that you can form with different question words:
кто бы ни пришёл (whoever comes), где бы ты ни был (wherever you are), etc.

Why is бы written separately here? Why not чтобы?

Чтобы (one word) is a conjunction meaning in order to / so that or introducing subordinate clauses with that:

Я учу русский, чтобы говорить с друзьями. – I study Russian in order to speak with friends.

In что бы ни случилось, you have что (what) + бы (particle). They are not forming чтобы, so they must be written separately:

что бы ни случилось – whatever happens
чтобы случилось... – would sound wrong here; this is not a purpose clause.

When you see что бы followed by ни and a past-tense verb, it will almost always be this что + бы pattern, not the conjunction чтобы.

What is the role of ни in что бы ни случилось?

Ни in this construction serves as an intensifying, “negative-like” particle that helps create the meaning no matter what / regardless of what.

Patterns:

что бы ни случилось – no matter what happens
кто бы ни пришёл – no matter who comes
где бы ты ни был – no matter where you are

You can think of бы ... ни as a frame around the verb that marks a concessive / “whatever, whoever, wherever” meaning. You cannot omit ни in this meaning:
✗ что бы случилось – is not idiomatic for whatever happens.

Why is случилось in the past tense if the meaning is “no matter what happens (during the day)”?

In Russian, hypothetical or general conditions are often expressed with:

бы + verb in past tense → if / should / whatever happens

So grammatically it looks past, but functionally it is irrealis (hypothetical, not real time):

Если бы что‑то случилось, я бы позвонил. – If something happened, I would call.
Что бы ни случилось, я приду. – Whatever happens, I will come.

Случилось here is neuter past (matching что), but because of бы and ни, the whole phrase means no matter what may happen / might happen, not “no matter what happened” in the real past.

Why do we say днём and вечером instead of день and вечер?

Forms like утром, днём, вечером, ночью are adverbial uses of the instrumental case that mean in the morning / in the daytime / in the evening / at night.

So:

днём – during the day / in the daytime
вечером – in the evening

You could in theory say things like в течение дня, в этот вечер, but for simple “when?” with time of day, Russian very often uses these instrumental forms as adverbs.

So the sentence structure is:

Что бы ни случилось днём – whatever happens during the day
вечером мне хочется... – in the evening I feel like...

What does всё равно add to the meaning? Could we omit it?

Всё равно roughly means anyway / regardless / still / it makes no difference.

In вечером мне всё равно хочется немного тишины, it emphasizes that even if the day was quiet, loud, stressful, boring – regardless of what the day was like, in the evening the speaker still wants some quiet.

Without всё равно: вечером мне хочется немного тишины – in the evening I want some quiet.
With всё равно: there is a stronger sense of no matter what happened before, the result is the same.

So grammatically you can omit it, but you will lose that “regardless of circumstances” nuance that ties it to the first clause.

Why is it мне хочется, not я хочу?

Both are correct Russian, but they differ in style and nuance.

Я хочу немного тишины. – I want some quiet.
More direct and volitional: “This is what I want.”
Мне хочется немного тишины. – I feel like having some quiet.
More impersonal and softer: it sounds like this desire arises in me by itself.

Хочется is an impersonal verb form (same form as 3rd person singular), used with a dative:

мне хочется – I feel like / I want
тебе хочется – you feel like / you want
ему хочется – he feels like / he wants

It’s similar to Russian patterns like:

мне холодно – I am cold (literally “to me, it is cold”)
мне грустно – I feel sad

So мне хочется немного тишины is a natural, softer way to talk about a spontaneous desire or need.

Why is the verb хочется and not хочу or хочет? What form is this?

Хочется is the impersonal form of хотеться, which behaves like a 3rd person singular form, but with no clear subject.

Pattern:

Мне хочется спать. – I feel like sleeping.
Нам хочется отдыха. – We feel like having a rest.

Structurally:

мне – dative (“to me”)
хочется – impersonal verb (“it is wanted / one feels like it”)
немного тишины – what is desired

Using хочу would change the structure:

Я хочу немного тишины. – subject я
- verb хочу
  - object.

So хочется marks that we’re using the impersonal “it is wanted by me” type of construction.

Why is it немного тишины in the genitive, not немного тишина?

Numbers and quantifiers like много, мало, немного, столько, сколько normally require the genitive case of the noun:

немного воды – a little water
немного времени – a little time
немного тишины – a bit of quiet / of silence

So:

тишина – nominative (dictionary form)
тишины – genitive singular

After немного, тишины must be in the genitive.
✗ немного тишина is grammatically wrong.

What is the nuance of тишины here? Why not use тихо or тише?

Different words, related meanings:

тишина – noun “silence, quiet(ness)”
немного тишины – a bit of quiet; some quiet.
тишины – genitive singular of тишина (required after немного).
тихо – adverb “quiet(ly)”
Мне хочется, чтобы было тихо. – I want it to be quiet.
тише – comparative of тихий / тихо (“quieter”, or an imperative: be quieter!).

In the original sentence, the speaker wants some amount of quiet as a kind of “substance” or condition, so the noun тишина in genitive (тишины) fits perfectly:
немного тишины ≈ a little peace and quiet.

Can the word order be changed, for example to Мне вечером всё равно хочется немного тишины?

Yes, Russian word order is relatively flexible, and several variants are possible:

Вечером мне всё равно хочется немного тишины. (original)
Neutral, with a slight emphasis on in the evening at the beginning.
Мне вечером всё равно хочется немного тишины.
Puts light emphasis on мне (to me, personally) and then вечером.
Мне всё равно вечером хочется немного тишины.
Slightly unusual rhythm, but possible in speech; всё равно then вечером is less smooth.

The original word order is the most neutral and natural for written Russian here, especially since вечером neatly echoes днём from the first clause.

Are there similar expressions to что бы ни случилось with other words?

Yes, this is a productive pattern in Russian:

[question word] + бы + ни + [past tense verb] → no matter [who/what/where/when/how] ...

Common examples:

кто бы ни пришёл – no matter who comes
что бы ни говорили – no matter what they say
где бы ты ни жил – no matter where you live
когда бы он ни позвонил – no matter when he calls
как бы он ни старался – no matter how hard he tries

So что бы ни случилось днём fits into this broader pattern.

How would you stress the words in this sentence when speaking?

The natural stresses are:

Что́ бы ни случи́лось днём, ве́чером мне всё равно́ хо́чется немно́го тишины́.

Main sentence-level stresses:

Что́ бы ни случи́лось днём – stress on что́ and случи́лось
ве́чером мне всё равно́ хо́чется немно́го тишины́ – key stresses on ве́чером, равно́, хо́чется, тишины́

Intonationally, you usually:

Slightly raise and then fall at the end of днём (end of the first clause),
Then a small pause,
Then another rise-fall pattern over the second part, with тишины́ carrying the final fall.