Learn Hardcore Indonesian: Saya parkir mobil di garasi belakang rumah. - I park the car in the garage behind the house.

Saya parkir mobil is very common in everyday speech; the borrowed verb parkir is used directly without affixes.
Saya memarkir mobil is more formal/standard (with the meN- prefix).

Use the affixed form in writing or formal contexts; the bare form is fine in conversation.

What’s the difference between memarkir and memarkirkan?

memarkir [objek] = to park [something]. Neutral and standard: Saya memarkir mobil.
memarkirkan [objek] (di/ke tempat) can add a sense of “cause to be parked” or “park for someone (benefactive).” In practice, many speakers use memarkirkan interchangeably with memarkir: Saya memarkirkan mobil di garasi. Prescriptive grammars sometimes prefer memarkir here, but both are widely used.

Why is it di garasi, not ke garasi, if I moved the car there?

di marks the final location (where something ends up): Saya memarkir mobil di garasi.
ke marks movement toward a destination: Saya mengarahkan/memasukkan mobil ke garasi. For parking, Indonesian usually focuses on the end location with di. If you want to emphasize movement into the garage, switch the verb and use ke.

Does mobil here mean “my car” or “a car”? How do I show that?

Indonesian has no articles, so mobil can be “a car,” “the car,” or even “my car,” depending on context. To be explicit:

“my car”: mobil saya / mobilku
“the car (specific)”: mobil itu
“a car (introducing one)”: sebuah mobil (used when you really need to stress indefiniteness)

Should it be rumah saya instead of just rumah to mean “my house”?

You can add a possessor if needed:

di garasi belakang rumah saya (explicitly “my house”) But Indonesian often omits the possessor when it’s obvious from context. Alternatives:
rumahku (informal), rumah kami/kita (our house; kami = excluding listener, kita = including listener), rumahnya (his/her/the house’s).

What exactly is belakang here—an adjective or a preposition? Could I say di belakang rumah?

belakang is a location noun meaning “the back/rear.” It appears in two common patterns:

As a noun in a prepositional phrase: di belakang rumah = “behind the house.”
As a post-nominal modifier: garasi belakang = “the back/rear garage.” In your sentence, garasi belakang rumah compresses “garage [at] the back of the house.”

Does garasi belakang rumah mean “the back garage of the house” or “the garage behind the house”? Is there ambiguity?

It usually means “the garage at the back of the house,” but it can be read either way. To disambiguate:

“garage behind the house”: garasi di belakang rumah or garasi yang berada di belakang rumah
“the back/rear garage (of the house)” (e.g., there’s a front and a back garage): garasi belakang rumah itu or garasi bagian belakang rumah

Can I reorder the location bits, like Saya parkir mobil di belakang rumah, di garasi?

Yes. Natural variants include:

Saya parkir/memarkir mobil di garasi di belakang rumah (saya).
Saya parkir mobil di belakang rumah, di garasi.
Topicalization is also possible: Mobil saya saya parkir di garasi belakang rumah. All are grammatical; choose based on what you want to emphasize.

How do I show past tense, like “I parked the car …”? Indonesian has no tenses, right?

Correct—no tense inflection. Use time words/aspect markers:

Completed: Saya sudah memarkir mobil … / Saya tadi memarkir mobil … / Saya baru saja memarkir mobil …
With a time adverb: Saya memarkir mobil tadi malam / kemarin / barusan.

Can I drop the subject and say Parkir mobil di garasi belakang rumah?

You can drop subjects in Indonesian, but bare Parkir mobil … is easily heard as an imperative (“Park the car …”). To state a completed action without the subject, add context markers:

Sudah parkir mobil di garasi belakang rumah.
Tadi parkir mobil di garasi belakang rumah. These read as statements, not commands.

Is di here the preposition or the passive prefix di-? How can I tell?

It’s the preposition di meaning “at/in,” and it’s written with a space: di garasi. The passive prefix di- attaches directly to verbs with no space: diparkir, dimasukkan. So:

Preposition: di garasi
Passive verb: Mobil itu diparkir di garasi …

How do I say “The car is parked in the garage behind the house”?

Common options:

Passive (someone parked it): Mobil itu diparkir di garasi belakang rumah.
Stative/result (emphasizes the state): Mobil itu terparkir di garasi belakang rumah. If you mean “is being parked (right now),” add aspect: Mobil itu sedang diparkir …

Is Saya the best pronoun here? When would I use aku or gue?

Saya: neutral–polite, safe in most situations (work, with strangers, mixed company).
aku: informal/intimate (friends, family, lyrics).
gue/gua: very informal, Jakarta/urban slang. Match the pronoun to your relationship and setting: Saya is safest unless you’re sure an informal register is appropriate.