Learn Hardcore Russian: Глубокий сон после тяжёлого дня помогает забыть про нервные мысли. - Deep sleep after a hard day helps you forget nervous thoughts.

The noun день is masculine singular.
After после, день becomes genitive singular: дня.
The adjective тяжёлый must match the noun, so it also changes to masculine singular genitive: тяжёлого.

So you get после тяжёлого дня (after a hard day), not после тяжёлый день (which is ungrammatical).

Why is сон the subject, and can the word order be changed?

In this sentence, сон (sleep) is the grammatical subject, and помогает (helps) is the verb:

Глубокий сон … помогает … → Deep sleep … helps …

Russian allows flexible word order. You could also say:

После тяжёлого дня глубокий сон помогает забыть про нервные мысли.
Глубокий сон помогает после тяжёлого дня забыть про нервные мысли.

All of these are grammatical; the changes mostly affect emphasis. The original version emphasizes глубокий сон at the beginning.

Why is помогает in the present tense and imperfective, not поможет?

Помогает is present tense, imperfective, and here it describes a general, habitual truth:

Глубокий сон … помогает … = Deep sleep (generally) helps …

If you used поможет (future, perfective):

Глубокий сон … поможет забыть…

this would sound more like a specific future instance: “A deep sleep (this time) will help you forget…”

So помогает gives a general statement, like a proverb or general observation.

Why is the second verb забыть (perfective) and not забывать?

In constructions like помогать + infinitive, Russian often uses the infinitive that best matches the intended result:

забыть (perfective) = to forget (as a completed action, to manage to forget)
забывать (imperfective) = to be forgetting / to forget repeatedly / habitually

Here the idea is that deep sleep helps you achieve the state of having forgotten those thoughts, a completed result. So забыть is natural:

помогает забыть = helps (you) to forget (successfully / completely)

What exactly does про mean in забыть про нервные мысли, and is it the same as о?

Про is a preposition that usually means about or concerning and takes the accusative case:

про мысли → about thoughts (accusative plural)

In this expression:

забыть про нервные мысли ≈ “forget about nervous thoughts”

You could also say:

забыть о нервных мыслях

Differences:

про + accusative (про нервные мысли) is more colloquial / everyday.
о + prepositional (о нервных мыслях) is more neutral or formal.

Both are correct here; the sentence with про just sounds more conversational.

Why are мысли and нервные in the forms нервные мысли, not something like нервных мыслей?

Because after про you need the accusative case, and the phrase is plural:

Nominative plural: нервные мысли
Accusative plural (for inanimate nouns) is the same as nominative plural: нервные мысли

So:

про нервные мысли = about nervous thoughts (accusative plural)

If you used о, then you would need the prepositional case:

о нервных мыслях (prep. plural)

Is про нервные мысли an idiomatic phrase? Could I just say забыть нервные мысли?

Про adds the idea of “about” — forget about something, stop thinking about it.

забыть нервные мысли = to forget the nervous thoughts (more literal/rare; sounds a bit strange, like you “possess” them as an object)
забыть про нервные мысли = to forget about nervous thoughts, to stop worrying about them (natural)
забыть о нервных мыслях = same meaning, more neutral/formal

So in everyday speech, забыть про нервные мысли is the most natural way to say it.

Why is it глубокий сон and not another adjective like крепкий сон?

Both are possible, but they have slightly different nuances:

глубокий сон = deep sleep (emphasis on the depth, that you are “far away” from wakefulness and thoughts)
крепкий сон = sound, strong sleep (emphasis on quality and undisturbed sleeping)

In the context of “helping to forget nervous thoughts,” глубокий сон is very natural, because it suggests you are deeply immersed in sleep, away from your worries. Крепкий сон would also work, just with a slightly different feel.

How do you pronounce глубокий, тяжёлого, and мысли? Where is the stress?

глубо́кий: [glu-BO-kiy]
- Stress on the second syllable: гла бо́ кий
тяжёлого: [tya-ZHYO-lo-va]
- Stress on жё: тя жо́ лого
- The ё is always stressed and pronounced “yo”
мысли: [MYS-lee]
- Stress on the first syllable: мы́сли
- ы is a central vowel (not “i”); tongue is further back than in English “ee”.

Could I say после тяжёлого дня помогает глубокий сон instead? Does that change the meaning?

Yes, you can say:

После тяжёлого дня помогает глубокий сон.

Grammatically it’s fine. The meaning is essentially the same, but the focus shifts:

Глубокий сон после тяжёлого дня помогает…
→ Emphasis starts on “deep sleep” as the key thing.
После тяжёлого дня помогает глубокий сон.
→ Emphasis starts on the time-situation (“after a hard day”), and then introduces deep sleep as the helper.

Both are good natural Russian sentences.

Why do all the adjectives change endings: глубокий, тяжёлого, нервные?

Adjectives in Russian must agree with the noun in:

Gender (masc./fem./neut.)
Number (singular/plural)
Case (nominative, genitive, etc.)

In this sentence:

сон: masculine, singular, nominative
- → глубокий сон (masc. sg. nom.)
день after после: masculine, singular, genitive (дня)
- → тяжёлого дня (masc. sg. gen.)
мысли after про: plural, accusative (same form as nominative plural: мысли)
- → нервные мысли (pl. acc./nom.)

The different endings (-ий, -ого, -ые) show those agreements.