Breakdown of Вы когда-нибудь организовывали туры в Австралию?
вы
you (plural or formal)
в
in / to (direction)
когда-нибудь
ever / sometime
тур
tour
Questions & Answers about Вы когда-нибудь организовывали туры в Австралию?
Since organizing a tour is a completed action, why use the imperfective организовывали instead of the perfective организовали?
This perfectly illustrates the "General Factual" meaning of the imperfective. Whenever you ask "Have you ever done X?" using когда-нибудь, you are asking about the mere fact of an experience occurring at some point in someone's life. Because you aren't focusing on the result of one specific, concrete event, you must use the imperfective past tense.
How is the perfective form of this verb different from the imperfective?
The imperfective verb used here is организовывать. Its perfective pair is организовать. The key difference is the -ыва- suffix in the imperfective, which gives us the past tense организовывали. If you were asking if they successfully organized one specific upcoming or past event, you would drop the suffix and use the perfective past tense: организовали.
Could I use когда-то instead of когда-нибудь in this sentence?
No. когда-нибудь means "ever" and is the standard choice for questions asking if an event has happened at any unspecified point in time. когда-то means "once" or "formerly" and is almost exclusively used in statements to refer to a specific, but perhaps forgotten or no longer relevant, time in the past (e.g., "I used to live there когда-то").
Why is Australia in the Accusative case (в Австралию) rather than the Prepositional (в Австралии)?