Learn Hardcore Russian: Я вышел из гаража и закрыл дверь. - I went out of the garage and closed the door.

выйти (past masc: вышел) = to go out of an enclosed space (through a door, out of a room, etc.). It pairs naturally with из.
уйти (past masc: ушёл) = to leave/go away from a place in general. With a garage (an enclosed space), вышел из гаража is the most direct and specific. Ушёл из гаража is possible but emphasizes departure rather than the act of coming out.

Why is it из гаража? What case is гаража?

Из is used for movement out of/from the inside of something and takes the genitive. Гаража is the genitive singular of гараж (masc. inanimate). So: из + Genitive → из гаража.

Could I use с or от instead of из?

с is used for movement off a surface or away from certain places/events (e.g., с крыши, с концерта, с работы). Not right here.
от means “(away) from” a point/person/object (e.g., от дома = away from the house). To say “out of the garage,” you need из.

What aspect are the verbs? Could I use imperfective?

Both are perfective: вышел (pf of выйти) and закрыл (pf of закрыть), showing completed, sequential actions. Imperfective variants:

выходил = was going out/used to go out (process/habit)
закрывал = was closing/used to close (process/habit) Example of habit: Я выходил из гаража и закрывал дверь каждый вечер.

How does the sentence change if the speaker is female or plural?

Female: Я вышла из гаража и закрыла дверь.
Plural: Мы вышли из гаража и закрыли дверь.

What case is дверь, and why doesn’t it change?

Дверь is the direct object, so accusative singular. For inanimate feminine nouns like дверь, accusative = nominative, so it stays дверь (not “двери”).

Why not дверью?

Дверью is instrumental singular (“with/by means of the door”). Закрыть дверь = “to close the door.” Закрыть дверью would mean “to close (something) with a door” (e.g., “He closed the opening with a door”), which is different.

Would ворота be more natural for a garage door?

Often yes. Many garage “doors” are gates (ворота, plural-only noun). Then you’d say: …и закрыл ворота. If you mean a small side door, дверь is correct.

Is the pronoun Я necessary?

Not strictly. You can say Вышел из гаража и закрыл дверь. In the past tense, the verb form shows gender/number (вышел = masculine singular), so the subject is recoverable from context. Using я is common, especially at the start of a narrative.

Where is the stress? How do I pronounce the sentence?

Stressed version: Я вы́шел из гаража́ и закры́л дверь.

вы́шел: stress on the first syllable; ш is always hard.
гаража́: stress on the last syllable.
закры́л: stress on -рыл-.
дверь: the final ь softens the preceding р.

Why is it вышел (with е) and not вышёл (with ё)?

Because ё is always stressed. In вы́шел, the stress is on the first syllable, so the last syllable is unstressed and written with е, not ё. Compare: шёл, пошёл, нашёл (stress on ё).

Do I need a comma before и?

No. Two predicates share the same subject (я) and are joined by и: Я вышел… и закрыл… No comma is used in Russian in this case.

Does и here imply “and then,” or do I need потом?

With perfective verbs in narrative, и naturally implies sequence (“and then”). Потом/затем can be added for emphasis: Я вышел из гаража, потом закрыл дверь.

Can I swap the order: Я закрыл дверь и вышел из гаража?

Grammatically yes, but it suggests he closed the door first and then left—world-knowledge makes that odd unless, say, there’s a remote control or another exit. The original order matches the likely real-world sequence.

How do I say “closed the door behind me”?

Add за собой: Я вышел из гаража и закрыл за собой дверь.

Could I use the reflexive verb: дверь закрылась?

That describes the door closing by itself or as a result of something else: Дверь закрылась. Your sentence needs an active transitive action: я закрыл дверь (“I closed the door”).