Kan du lägga pappren i ordning innan chefen kommer?

It can be both, but in this sentence it is most naturally a polite request.

• Kan du lägga pappren i ordning ... ? = Can you put the papers in order ... ?
• In everyday Swedish, kan du ... ? often works like English Can you ... ? when asking someone to do something.

So grammatically it asks about ability, but pragmatically it often means Please do this.

Because it comes after the modal verb kan.

In Swedish, modal verbs such as:

• kan = can
• ska = shall / will / be going to
• måste = must
• vill = want to

are followed by the infinitive without att.

So:

• kan lägga = can put
• not kan lägger
• not kan att lägga

Because after a modal verb like kan, Swedish normally does not use att.

Compare:

• Jag vill läsa. = I want to read.
• Hon kan komma. = She can come.
• Du måste gå. = You must go.

So kan du lägga ... ? is completely normal.

Pappren means the papers.

It is the definite plural form of papper.

Basic forms:

• ett papper = a paper
• papper = papers
• pappren = the papers

A learner may also come across papperen. Pappren is a common shortened form. In this sentence, it simply means the papers.

I ordning means in order, tidied up, or arranged properly, depending on context.

In this sentence:

• lägga pappren i ordning

means something like:

• put the papers in order
• arrange the papers neatly
• sort the papers out

It is an idiomatic expression, so it is best learned as a chunk:

• lägga något i ordning = put something in order

Because chefen means the boss.

The ending -en marks the definite singular of many common gender nouns.

So:

• en chef = a boss
• chefen = the boss

Since the sentence refers to a specific boss, Swedish uses the definite form.

Swedish often uses the present tense to talk about the future, especially when the future event is clear from context.

So:

• innan chefen kommer = before the boss comes

Even though the coming happens in the future, kommer is perfectly normal.

English does something similar in time clauses:

• before the boss comes not
• before the boss will come

So this is very natural Swedish.

Because innan introduces a subordinate clause.

In a subordinate clause, Swedish normally keeps subject + verb order:

• innan chefen kommer
• när hon kommer
• om du vill

You do not use question word order there.

So:

• kommer chefen? = Is the boss coming?
• innan chefen kommer = before the boss comes

Those are different structures.

Because this is a yes/no question.

In Swedish main clauses, the finite verb usually comes in the second position. But in yes/no questions, the finite verb comes first:

• Du kan lägga pappren i ordning. = You can put the papers in order.
• Kan du lägga pappren i ordning? = Can you put the papers in order?

So the verb moves in front of the subject to form the question.

Yes, often you could, and the meaning would be very similar.

• lägga pappren i ordning = put the papers in order
• ordna pappren = arrange the papers / sort out the papers

The version with i ordning sounds a bit more like physically putting them into a proper order. Ordna is slightly more general. In many contexts, either would work.

It can do both.

In your sentence, innan is followed by a clause:

• innan chefen kommer = before the boss comes

But it can also be followed by a noun phrase in some contexts:

• innan mötet = before the meeting
• innan lunch = before lunch

So innan works a lot like English before.

It is neutral everyday Swedish.

• Kan du ... ? is polite and common
• lägga pappren i ordning sounds natural in ordinary speech or writing
• Nothing in the sentence is especially slangy or especially formal

So it would fit well in normal workplace Swedish.

It could mean either, depending on context.

Papper can refer to:

• actual sheets of paper
• documents
• paperwork

In this sentence, pappren most likely means the papers/documents that need to be arranged before the boss arrives. The exact meaning depends on the situation.