naeil jeonyeoge sikdang yeyageul miri jaba dueosseoyo.

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

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”

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.

-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)

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.

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.

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.

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)