Some questions about te oku and te aru

My understanding of te oku is it is 'in preparation' for something. Therefore the verb before it should be transitive. It SOMETIMES uses the particle for the noun. (But not always?)
Similarly, my understanding of te aru is it is 'something done by someone'. It almost always uses the particle ga, and it ALWAYS goes with a transitive verb.

I get a little confused with the conversation example below from my book. I have highlighted the answers I think are right - could somebody see how these make sense or not? I feel like a lot of these are inexchanagable - could anyone confirm this?

2. Choose the right word to complete the conversation.
A: もう飲み物は買って（ ある / おく）？
B: うん、買って（ある / おく）よ。きのう、安かったから買っておいたんだ。
A: へやもそうじして（ ある / おく）ね。
B: ５時間もかけてそうじしたんだ。でも、時間がな くて、すしは作って（ ある /
ない）んだ。
A: じゃあ、私が買いに行こうか？
B: いいよ、買うと高いし。ビデオは借りて（ ある / おく）？
A: まだなんだ。ビデオ屋に予約はして（ ある / おく）けど。
B: じゃあ、今から借りてきて。その間にすしを作っ て（ある / おく）から。

The fact I marked most of these randomly shows how confused I am with all of this

I think they are all right except,
A: まだなんだ。ビデオ屋に予約はして（ ある / おく）けど。

てある is very similar to ている, in that it's essentially a change in tense. It refers to something that has been done and remains that way, though, which is somewhat different from something that is continuously happening as in the case of ている.
In this sentence, it would be like saying 'The video is reserved at the store though.'

ておく is difficult to understand for native English speakers because in many cases it simply doesn't translate - the sentence with and without おく is often translated into the same English. However, it adds a sense of purpose and intent, and ておく refers to something that one is doing right now or is going to do. Of course, when something has already been done you can use ておいた as your dialogue does (though not as a question, oddly enough.)

Thanks so much, it's starting to make sense.

As for ～てある, the following thread might be somewhat helpful.

てある [Grammar] | Japan Forum