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Think about these cases:
1) A detective have found out a bunch of clues in the last three months. Now, he needs to spend two or three days to arrange/ summarize / absorb these clues to draw a conclusion.
2) A student spent a whole day in the school. That night at home he decided to arrange / summarize / absorb / digest what he learned that day.
What's the best word (or phrase) to describe the process to arrange some disorganized information to get a more thorough and deeper understanding?
Here's a simple suggestion that I think combines the meanings of all your options (arrange, summarise and absorb):
"1 Devote time and attention to gaining knowledge of (an academic subject), especially by means of books"
"1.1 Investigate and analyse (a subject or situation) in detail"
The sentences in your question could be phrased using the verb study as:
A detective have found out a bunch of clues in the last three months. Now, he needs to spend two or three days studying these clues to draw a conclusion.
A student spent a whole day in the school. That night at home he decided to study what he learned that day.
Your "arrange" and "summarize" have different meanings from "absorb" and "digest". As Damkerng has said, "organize" is a good word for "arrange some messed [up] information". (In fact, "disorganized" is a better word for "messed up".) To "get a more thorough knowledge" of something, you can "absorb", "digest", or "assimilate" it. That said, here's what I would write:
A detective has discovered a bunch of clues over the past three months. Now, he needs to spend two or three days organizing and absorbing (or "take two or three days to organize and absorb") them.
(Why we use the present participle with "spend" and the infinitive with "take" isn't clear to me. It's one of those things that you just have to learn, as far as I can see. Perhaps someone else can shed light on that.)
A student spent a whole day in the school. That night at home he decided to organize and absorb what he learned that day.
In your first example all words are appropriate to be used. I’d add to reason/deduce.
In your second example also all words are fine.
I think the close word to this is gist. Though it is not a process but it'll fulfill the purpose.
gist - the main or general meaning of a piece of writing, a speech or a conversation.
So, in your sentences...
However, others may come up with other words.
