Learn Hardcore Indonesian: Kunci cadangan saya simpan di laci meja.

Because this is the short passive (often called passive type 2): object + agent pronoun + bare verb. In that pattern you use the verb root: Kunci cadangan saya simpan....

Active: Saya menyimpan kunci cadangan...
di- passive: Kunci cadangan disimpan (oleh saya)...
Writing Kunci cadangan saya menyimpan... is ungrammatical.

Is the sentence active or passive?

Grammatically it’s the short passive (pasif 2). The object (kunci cadangan) is fronted, the agent is a pronoun (saya), and the verb is bare (simpan). Natural English often translates it as active.

Can I also say Saya menyimpan kunci cadangan di laci meja?

Yes. That’s the straightforward active form. It sounds neutral and a bit more formal than Saya simpan... in everyday speech.

What nuance does the given word order add?

Fronting the object puts focus on it, roughly “As for the spare key, I keep it in the desk drawer.” It’s common when the key is the topic or you’re contrasting it with other items.

Does saya here mean “my” or “I/me”?

Here saya is the agent pronoun “I/me,” not a possessive. The sentence does not explicitly mark possession of the key, though context often implies it.

How do I say it if I want to make “my spare key” explicit?

You can show both possession and agent:

Kunci cadangan saya saya simpan di laci meja. (possessor + agent, both are saya)
Or use clitics: Kunci cadanganku kusimpan di laci meja. (possessor = -ku; agent = ku-)

Is Kunci cadangan disimpan di laci meja (oleh saya) also correct?

Yes. That’s the di- passive. It sounds more formal; the agent phrase oleh saya is usually omitted unless needed for clarity or emphasis.

Why not use menyimpan after saya here?

Because in the short passive pattern the verb must be bare. If you switch to menyimpan, you must revert to normal active order: Saya menyimpan kunci cadangan...

What exactly does kunci cadangan mean? Why is the order “key spare,” not “spare key”?

Indonesian noun–noun compounds are head-first: kunci (head) + cadangan (modifier) = “reserve/spare key.” This is the normal pattern (like toko buku “book store”).

Is kunci serep okay instead of kunci cadangan?

Yes. Kunci serep is very common in everyday speech. Kunci cadangan is a bit more neutral/formal. Both are widely understood.

Why di laci meja and not di dalam laci?

Both are fine:

di laci = in/at the drawer (default)
di dalam laci = explicitly “inside the drawer” (extra emphasis on interior)

Does meja mean “desk” or “table”? Is di laci meja natural?

Meja covers both “table” and “desk.” Di laci meja is natural and means “in the desk/table drawer.” If you want to specify “desk,” you can say meja kerja or meja tulis.

How do I mark “the/that” spare key?

Use demonstratives or -nya:

Kunci cadangan itu saya simpan di laci meja. (that/the spare key)
Kunci cadangannya saya simpan di laci meja. (definite; can also mean “his/her/its” depending on context)

What’s the difference between di as a preposition and di- as a verb prefix?

di (separate word) is a preposition for locations: di laci, di rumah.
di- (attached) is the passive verb prefix: disimpan, dibawa.
Don’t write a space for the prefix: disimpan is correct, di simpan is not.