それで, それと, それから, あと(は), and そのほかに: The difference

Question

I'm doing a practice book that tends to oversimplify things for the sake of... simplicity. In one of the questions, the following sentence is given:

柿をください。それと、イチゴも。＿＿、ドリアンも。

The provided two similar options, あと・それで, with the former being the answer.

I'd always thought that それで can fill in any place where I wish to express "and then," so I chose the latter.

In the explanation section, they say that それと = それから, and あと = それほかに.

They also gave these two sample sentences:

登山はちょっと…。時間がないし…、それと体力もないし…。
宿題はしたし、掃除もしたし、あと何をしたらいいかな。

In addition to それで, I had always thought that the following conjunctions are interchangeable: それで, それから, and あと(は) (didn't know that それと existed). As mentioned above, there's also そのほかに, which I feel do not differ significantly from them. This thesaurus confirms my assumption それからの同義語 about most of them bar それで.

Question:
How are these similar terms used differently? How does one decide when to use which? I'm especially keen on knowing why それで does not work in the question sentence. If these's really no way of explaining the subtlety, I'll take "time and exposure" for an answer.

Edit 1:
Thanks to user4092様's comment, I think それで is out of the way now. However, are それと, それから, あと(は), and そのほかに interchangeable in the sentence at the top? Can I switch them around? For example, can I say

Aをください。あと、B。それから、Cも。

or

Aをください。そのほかに、B。それから、Cも。

Edit 2:
それかれ was an awful typo on my part obviously. My apologies. (Apparently, it exists tho.)

どうぞよろしくお願いいたします！

Answer 1

それで

１ 前述の事柄を受けて、それを理由としてあとの事柄を導く場合に用いる。それだから。それゆえ。そういうわけで。「納得できなくて、それでまた質問したのです」

２ 前の事柄を受けて、話題を他に転じたり、相手に話を促したりするときに用いる。そして。「それで、これからどうしようか」「それで、どうなったの」

Basically it says that it is either used to "justify something", or to "change/make the conversation progress".

In English, "so" has the same usage so I think it's a good translation.

それでまた質問したのです : So I asked a question (which is why I asked a question)

それで、どうなったの : So, what happened? (and? what happened?)

それと

１ 物事を付け加える際に用いる接続詞的表現。「それ」は前述の事柄を指す。「それと、お花に水もあげといて」などのように用いる。

It says that it is used to add something (an action, object etc) to one another.

それと、お花に水もあげといて : With that, give the flower some water (also, give the water some water)

それかれ

１ 不定称。その名をいわずに二人以上の人をさしていう語。だれそれ。だれとだれ。 「院の殿上には誰誰かありつると人の問へば，－など四五人ばかりいふに／枕草子 108」 

It says that it is used to refer to more than 2 people without using their names. This one doesn't really have anything to do with the others but I include it anyway.

あと(は)

１ （接続詞的に用いて）それから。「後、気付いたことはありませんか」

I think this one is the easiest of all because the meaning is basically 後s meaning (after, then). The only thing to remember is that it doesn't necessarily mean "after" like if you were referring to an event that happened after a first one as in "I will go after I finish this" but it can also mean something like "and" as in 後は・・・これ！ (= And... this!!). So it has a really broad meaning.

そのほかに

This one means something like "other than that" and is pretty literal so you shouldn't have problems understanding it.

Now if we take your sentence:

柿をください。それと、イチゴも。＿＿、ドリアンも。

From what user4092 added and the definitions, we can definitely say that それで wouldn't fit there.

それと would. Because the それ would be referring to the previous element (イチゴ) and と would mean something like "with". That being said, I feel like it would be very weird as it has already been used two words before. So definitely not the best answer here even though it wouldn't be incorrect.

それかれ wouldn't.

そのほかに wouldn't in my opinion. It feels too long for such a simple sentence, especially with the それと that was used in the previous one.

The best one would definitely be あと since it is much more productive and simple.