Learn Hardcore Russian: Телефон мешает мне засыпать вечером. - The phone prevents me from falling asleep in the evening.

In this sentence, the idea is that the phone prevents the speaker from falling asleep, not from sleeping in general. So засыпать is the correct choice:

Телефон мешает мне засыпать. – The phone keeps me from falling asleep.
Телефон мешает мне спать. – The phone keeps me from sleeping (being asleep).

Both are possible, but they describe slightly different things.

Is засыпать here imperfective or perfective, and why?

In this sentence засыпать is imperfective.

Imperfective: засыпа́ть – to be falling asleep, to fall asleep in general, habitually, or as a process.
Perfective: засну́ть – to fall asleep (one completed act).

The construction мешать + infinitive normally uses the imperfective infinitive to talk about a general or repeated action:

Телефон мешает мне засыпать вечером.
The phone generally / regularly prevents me from falling asleep in the evenings.

You would not say мешает мне заснуть in this habitual/general sense; заснуть would sound like one specific occasion.

I’ve seen засыпать with different stress. What’s the difference between засыпа́ть and за́сыпать?

Stress completely changes the verb:

засыпа́ть (stress on the last syllable) – to fall asleep (imperfective)
- Я долго засыпа́ю. – I take a long time to fall asleep.
за́сыпать (stress on the first syllable) – to pour, to cover with something (like sand, earth, sugar)
- Он за́сыпал сахар в чай. – He poured sugar into the tea.
- Снег за́сыпал дорогу. – Snow covered the road.

In Телефон мешает мне засыпать вечером, the correct form is засыпа́ть (to fall asleep).

Why is it just вечером without a preposition like в вечером?

Вечером is the instrumental singular of вечер used in an adverbial sense, meaning in the evening / at night (in the evenings).

Russian often uses bare case forms (no preposition) to express time:

утром – in the morning
днём – in the daytime
вечером – in the evening
ночью – at night

You never say в вечером; that’s incorrect. You can, however, say:

в вечернее время – in the evening time (more formal/wordy)
по вечерам – in the evenings (regularly, every evening or many evenings)

Could I say Мне телефон мешает засыпать вечером? Is that still correct?

Yes, that sentence is grammatically correct.

Russian word order is flexible. Both:

Телефон мешает мне засыпать вечером.
Мне телефон мешает засыпать вечером.

are fine. The difference is in emphasis:

Телефон мешает мне… – neutral, subject (телефон) is slightly more in focus.
Мне телефон мешает… – puts more emphasis on мне (to me), e.g. “It’s me that the phone bothers (even if others are fine)”.

In many everyday contexts they will sound almost the same.

Can I drop мне and just say Телефон мешает засыпать вечером?

Yes, you can. Телефон мешает засыпать вечером is also grammatically correct.

With мне:
Телефон мешает мне засыпать вечером. – It explicitly says the phone keeps *me from falling asleep*.
Without мне:
Телефон мешает засыпать вечером. – More general/impersonal: The phone makes it hard to fall asleep in the evening (for me, or for people in general; context decides).

Dropping the dative pronoun often makes the statement sound more general or more like a complaint about the situation.

What exactly does мешать mean here? Is it like “mix” or “stir”?

The verb мешать has several meanings, depending on context:

to disturb / to bother / to prevent (with dative):
- мешать кому делать что – to prevent someone from doing something
- Телефон мешает мне засыпать. – The phone keeps me from falling asleep.
to mix / to stir (with a direct object, often food, liquids, etc.):
- мешать суп – to stir the soup
- мешать краски – to mix paints

In this sentence it’s clearly the first meaning (to disturb, to prevent) because:

it takes мне (dative), not a direct object
it’s followed by an infinitive засыпать (an action being prevented)

Is телефон here specifically a “phone call” or the physical phone/smartphone?

Телефон can mean:

the physical device (phone, smartphone), or
the telephone as a communication means, or
a phone call (by context).

In Телефон мешает мне засыпать вечером, most natural readings are:

the device itself (notifications, light, scrolling social media), or
phone use in general in the evening.

Context would clarify, but a native speaker will usually imagine the smartphone being the problem.

What’s the stress and pronunciation of each word in this sentence?

Телефо́н – te-lee-FON (stress on -фон)
меша́ет – mee-SHA-yeht (stress on -ша́-)
мне – mnye (one syllable, like “mnyeh”)
засыпа́ть – za-sy-PAT' (stress on -па́ть, final syllable)
ве́чером – VE-che-ram (stress on ве́-)

So the main stressed syllables in sequence are: телефо́н – меша́ет – засыпа́ть – ве́чером.