Learn Hardcore Russian: Наш самолёт обычно вылетает утром. - Our plane usually departs in the morning.

Наш – possessive pronoun our, masculine, singular, nominative; it agrees with самолёт in gender, number, and case.
самолёт – noun plane / airplane, masculine, inanimate, singular, nominative; this is the subject.
обычно – adverb usually; it modifies the verb вылетает.
вылетает – verb takes off / departs (by plane), 3rd person singular present, imperfective aspect, from вылетать.
утром – instrumental case of утро (morning), used adverbially to mean in the morning (time expression).

So grammatically it is:
[our] [plane] [usually] [takes off] [in-the-morning].

Why is it наш самолёт and not наша самолёт?

In Russian, possessive pronouns agree with the noun they modify in gender, number, and case.

самолёт is masculine (он, not она or оно).
The masculine nominative form of наш is наш.
наша is feminine nominative and would be used with feminine nouns like наша машина (our car).

So:

наш самолёт – correct (masculine noun)
наша самолёт – incorrect (gender mismatch)

Is it necessary to say наш here, or can I just say Самолёт обычно вылетает утром?

You can absolutely say:

Самолёт обычно вылетает утром.

That would usually be understood as The plane usually takes off in the morning, where which plane is clear from context (e.g., the flight you are talking about).

Adding наш:

Наш самолёт обычно вылетает утром.

adds the nuance our plane, i.e., the one we are flying on, or the one that belongs to our airline / our group, depending on context.

So наш is not grammatically required; it just adds a possessive nuance.

Why is вылетает in the present tense if we are talking about a schedule (which feels future)?

Russian works similarly to English here: the present tense of an imperfective verb is used for:

regular, habitual actions, and
scheduled future events.

So:

Наш самолёт обычно вылетает утром.
→ Our plane usually takes off in the morning (habit / schedule).

You can also use this for a specific scheduled future:

Самолёт вылетает завтра утром.
→ The plane takes off / leaves tomorrow morning.

So the present tense вылетает naturally covers both habitual and scheduled future, just like English leaves, takes off in timetables.

What is the difference between вылетает and вылетит?

Both come from the pair вылетать / вылететь (to take off / to depart by air):

вылетает – imperfective, present tense, 3rd person singular.
- Focus on process, regularity, schedule:
  - Наш самолёт обычно вылетает утром.
  - Our plane usually takes off in the morning.
вылетит – perfective, future tense, 3rd person singular.
- Focus on the single, completed event in the future:
  - Самолёт вылетит завтра утром.
  - The plane will take off tomorrow morning.

In your sentence, обычно (usually) describes a repeated / habitual action, so the imperfective вылетает is the natural choice.
Using вылетит with обычно would be wrong.

How do you conjugate вылетать in the present tense?

Вылетать is a regular -ать verb. Present-tense conjugation:

я вылетаю – I take off / I am flying out
ты вылетаешь – you (singular, informal) take off
он / она / оно вылетает – he / she / it takes off
мы вылетаем – we take off
вы вылетаете – you (plural or formal) take off
они вылетают – they take off

In the sentence Наш самолёт обычно вылетает утром, we have он вылетает (3rd person singular).

Why do we say утром and not в утро or just утро?

Утром is the instrumental case of утро, and in Russian the instrumental of parts of the day is commonly used adverbially to mean in the …:

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

So:

Наш самолёт обычно вылетает утром.
→ Our plane usually takes off in the morning.

Saying в утро is generally unnatural for this meaning. You might see phrases like:

в то утро – on that morning (narrative, specific morning),

but for generic in the morning as a time of day, you should use утром, not в утро.

Can the word order change? For example, can I say Обычно наш самолёт вылетает утром?

Yes, Russian word order is relatively flexible, and adverbs like обычно can move.

All of these are grammatical:

Наш самолёт обычно вылетает утром.
Обычно наш самолёт вылетает утром.
Наш самолёт вылетает утром обычно. (possible, but less common and more marked)

Most neutral/common choices:

Наш самолёт обычно вылетает утром.
Обычно наш самолёт вылетает утром.

The meaning remains Our plane usually takes off in the morning, though changing the position of обычно can slightly shift emphasis (e.g., starting with Обычно makes usually more prominent).

What is the difference between самолёт вылетает and самолёт улетает?

Both verbs involve a plane leaving, but the nuance differs:

вылетать / вылететь – to take off / to depart by air from somewhere (airport, city).
- Often used for official departures, schedules, timetables:
  - Самолёт вылетает в 9:00. – The plane departs at 9:00.
улетать / улететь – to fly away / to leave by plane, focusing more on the subject going away, not specifically the scheduled departure.
- Often used about people or the fact of leaving:
  - Он улетает завтра. – He is flying away tomorrow.

In a sentence about a scheduled departure like Наш самолёт обычно вылетает утром, вылетает is the most natural verb.

How would I say “Our plane usually takes off in the evenings / at night” using the same pattern?

You can keep the same structure and change the time expression:

Наш самолёт обычно вылетает вечером.
→ Our plane usually takes off in the evening.
Наш самолёт обычно вылетает ночью.
→ Our plane usually takes off at night.

Same pattern:

Наш самолёт (our plane)
обычно (usually)
вылетает (takes off)
вечером / ночью (in the evening / at night)

Is there any hidden subject like it in Russian, or is самолёт the subject?

Самолёт is the explicit subject; there is no extra pronoun like it.

Russian does not use dummy subjects like English it or there in such sentences. The structure is simply:

Наш самолёт – subject
обычно – adverb
вылетает – verb
утром – time expression

So you don’t say anything like Он наш самолёт… or add an it; самолёт alone is the subject.

How is the sentence pronounced, and where is the stress in each word?

Stresses (capital letters show the stressed vowels):

Нaш – one syllable; stress on a.
самолЁт – sa-mo-LYOT (stress on ё).
О́бычно – Ó-bych-no (stress on the first о; written обычно, but pronounced with reduced о /a/-like).
вылетАет – vy-le-TÁ-et (stress on а in -тает).
У́тром – Ú-trom (stress on у).

Approximate IPA:

Наш самолёт обычно вылетает утром
→ /naʂ sə.mɐ.ˈlʲot ɐ.ˈbɨt͡ɕ.nə vɨ.lʲɪ.ˈta.jɪt ˈu.trəm/

Natural speech will reduce some unstressed vowels, but keeping the stresses as above will make you sound clear and understandable.