Learn Hardcore Russian: Я успеваю сделать домашнее задание вечером. - I manage to do my homework in the evening.

It means “manage (in time)”/“have enough time within the schedule.” With a perfective infinitive like сделать, it implies you manage to complete the action within the available time. Natural translations: I manage to finish my homework in the evening; I have time to get my homework done in the evening.

Why is the infinitive сделать (perfective) used, not делать (imperfective)?

With успевать/успеть, a perfective infinitive highlights the result (completion). An imperfective infinitive focuses on the ongoing process or habit.

Я успеваю сделать домашнее задание вечером. = I manage to finish my homework in the evening.
Я успеваю делать домашнее задание вечером. = I have time to be doing my homework in the evenings (process; not necessarily finishing each time).

Could I say Я успею сделать домашнее задание вечером? How does it differ?

Yes. Успею (from perfective успеть) is the simple future: I will manage (this evening/tonight). The original успеваю (present, imperfective) is typically habitual or a general trend: I tend to manage to finish it in the evenings. If you specifically mean tonight, you can add сегодня вечером.

Why is вечером used without a preposition? Why not в вечером or в вечер?

Times of day are commonly used as prepositionless adverbials in the instrumental singular: утром, днём, вечером, ночью. Related options:

в этот вечер = on this particular evening
по вечерам = in the evenings (habitually)
к вечеру = by evening
до вечера = before evening

Can the word order change? For example, Вечером я успеваю сделать домашнее задание?

Yes. Russian word order is flexible; these are all natural, with slight differences in emphasis:

Вечером я успеваю сделать домашнее задание. (time is emphasized)
Я вечером успеваю сделать домашнее задание. (neutral)
Я успеваю вечером сделать домашнее задание. (slight focus on the verb + time) The core meaning does not change.

What case is домашнее задание, and why is the adjective домашнее (neuter)?

It’s accusative singular as the direct object of сделать. Задание is a neuter noun, so the adjective must agree in gender, number, and case: домáшнее задание. For inanimate nouns, accusative = nominative in form.

Do I need to say своё/моё (my) before домашнее задание?

Usually no; it’s understood from context. If you want to emphasize it’s your own, use своё домашнее задание (preferred and very natural). Моё домашнее задание is grammatically correct but can sound redundant in many contexts.

Is домашнее задание countable? When would I use the plural?

As a collective, домáшнее задание often means “homework” as a whole. Use plural домáшние задания for multiple distinct assignments (e.g., different tasks or subjects). In everyday speech, уроки can also mean “homework” collectively: делать уроки.

How do you pronounce key words, and where is the stress?

успеваю — успевáю (stress on -ва-).
сделать — сдéлать (stress on сдé-; the cluster сд is pronounced like [зд], so it sounds like “здé-”).
домашнее — домáшнее (stress on -ма-); задание — задáние (stress on -да-).
вечером — вéчером (stress on -ве-). Note: consonants before е, ё, ю, я, и are soft/palatalized.

What are the aspect pairs and basic forms for успевать/успеть?

Imperfective: успевáть — present: я успевáю, ты успевáешь, он/она успевáет, мы успевáем, вы успевáете, они успевáют; past: успевáл/успевáла/успевáли.
Perfective: успéть — future: я успéю, ты успéешь, он/она успéет, мы успéем, вы успéете, они успéют; past: успéл/успéла/успéли.

Do I have to use an infinitive after успевать? Can I say успеваю делаю?

Use the infinitive. Say успеваю сделать, not успеваю делаю. Two finite verbs together here are ungrammatical.

Can I omit я?

Yes: Успеваю сделать домашнее задание вечером. It’s grammatical. Russian often includes the pronoun for clarity, but dropping it is fine when the subject is clear from context or for a clipped style.

Are there more natural collocations than сделать домашнее задание?

Сделать домашнее задание is perfectly natural. Alternatives:

выполнить домашнее задание — more formal.
делать уроки — very common colloquial.
Colloquial nouns: домáшка; texting: ДЗ (abbreviation for “домашнее задание”).

How would I say it in the negative?

Я не успеваю сделать домашнее задание вечером. = I don’t manage to finish my homework in the evening. Keep домашнее задание after сделать (accusative).

How is Я успеваю сделать домашнее задание вечером different from simply Я делаю домашнее задание вечером?

Я делаю… states a routine fact: I do my homework in the evening. Я успеваю сделать… adds the nuance of time pressure and successful completion: despite a tight schedule, I manage to get it done in the evening.