Learn Hardcore Korean: naeil jeonyeoge sikdang yeyageul miri jaba dueosseoyo. - I made the restaurant reservation in advance for tomorrow evening.

It means “do something and leave it in that state for future benefit.” So 잡아 두었어요 = “(I) secured it and it’s now set/ready.” Morphology: 잡-아 두-었-어요 (grab/secure + put/keep + past + polite). Common parallels:

창문을 닫아 두다 = close the window and keep it closed
돈을 준비해 두다 = prepare money in advance

Is 미리 redundant if we already have -아/어 두다?

They overlap but aren’t identical. -아/어 두다 highlights doing something now so it remains useful later; 미리 explicitly says “in advance.” Using both emphasizes proactive planning.

예약을 해 두었어요 = I’ve set up the reservation (ready for later)
미리 예약했어요 = I booked in advance
미리 예약해 두었어요 = strongest “I proactively booked ahead and it’s set”

Why use 잡다 with 예약? How is 예약을 잡다 different from 예약하다?

예약하다 is the standard “make a reservation.”
예약을 잡다 is idiomatic and emphasizes “securing a slot/time.” Both are natural here:
식당 예약을 미리 했어요/해 두었어요
식당 예약을 미리 잡았어요/잡아 두었어요

How is -아/어 두다 different from -아/어 놓다? Can I say 잡아 놨어요?

Both mean “do something and keep/leave it that way.” Nuance:

-아/어 두다: more “for future convenience/benefit.”
-아/어 놓다: more “intentionally leave it that way” (state-focused). In this sentence, either is fine: 잡아 뒀어요 ≈ 잡아 놨어요.

What exactly does 저녁에 mark? Why not 내일에?

-에 marks a point in time. 저녁에 = “in the evening.” Words like 오늘/내일/어제 usually don’t take -에 on their own. You can say:

내일 저녁에 (very common)
내일 저녁 (dropping -에 is also fine in speech)

Does 저녁에 refer to when I made the booking, or when the reservation is for?

It refers to the time the reservation is scheduled for (tomorrow evening), not when you made the booking. The booking itself happened earlier, signaled by 미리 and -아/어 두다.

Is 식당 예약을 the best phrasing? Could I say 식당에 예약을?

Both are natural, with a small nuance:

식당 예약(을): compound noun “a restaurant reservation.”
식당에 예약(을) 하다: “make a reservation at the restaurant.” Your sentence’s 식당 예약을 is concise and idiomatic. This is also fine: 식당에 예약을 미리 해 두었어요.

Can I change the word order?

Yes, Korean word order is flexible. Keep the verb last and you’re safe:

내일 저녁에 식당 예약을 미리 잡아 두었어요 (neutral)
식당 예약을 내일 저녁에 미리 잡아 두었어요 (object focus)
미리 내일 저녁에 식당 예약을 잡아 두었어요 (adverb fronted) Meaning stays the same; you’re just shifting emphasis.

Any pronunciation or contraction tips?

두었어요 is almost always contracted to 뒀어요 in speech.
잡아 sounds like [자바].
저녁에 sounds like [저녀게].
식당 is often pronounced with tense assimilation: [식땅].

What level of politeness/register is 두었어요? Alternatives?

-었어요: polite informal (your sentence).
More formal: 잡아 두었습니다.
Casual: 잡아 뒀어. Contraction is normal: 두었어요 → 뒀어요.

How should I write the spacing: 잡아 두었어요 or 잡아두었어요?

Standard spacing writes auxiliary 두다/놓다 separately: 잡아 두었어요. In everyday writing you’ll also see 잡아두었어요. For tests or formal writing, prefer the spaced form.

Can I drop the object particle 을 after 예약?

Yes, in casual speech object markers are often omitted when context is clear:

식당 예약 미리 잡아 뒀어요 (casual) Keeping 을 is always safe and a bit more formal/clear: 예약을.

Are there other natural ways to say this?

Common alternatives:

내일 저녁에 식당 예약을 미리 해 두었어요.
내일 저녁에 식당 예약을 해 뒀어요.
식당에 내일 저녁으로 예약을 잡아 뒀어요. (using -으로 “for/as” that time)
Very colloquial: 식당 예약을 미리 넣어 놨어요. (put in a reservation)

What’s the difference between 예약 and 약속 here?

예약: a booking with a business/service (restaurant, hotel, hospital).
약속: an appointment/plan with a person. So for a restaurant you use 예약, not 약속.