Ons huiswerk is al af.

Because huiswerk is a het-word in Dutch: het huiswerk.

For singular het-words, the possessive our is ons:

• ons huis
• ons boek
• ons huiswerk

For de-words and for plural nouns, you use onze:

• onze auto
• onze tafel
• onze boeken

So:

• ons huiswerk = our homework
• onze huiswerken would only be possible if you were talking about multiple separate sets of homework, which is unusual.

In Ons huiswerk is al af, Dutch uses the verb zijn (to be) together with af to express the idea of something being finished.

So the structure is:

• iets is af = something is finished / done

Examples:

• Het eten is af. = The food is ready / finished.
• Mijn werk is af. = My work is done.
• Ons huiswerk is al af. = Our homework is already done.

English often uses be in the same kind of idea:

• The homework is done.

So this sentence is not using a verb meaning to finish. It is describing the state of the homework: it is finished.

Here, af means finished, done, or completed.

It is a very common Dutch word, and its meaning depends on context. In this sentence, af is part of the expression:

• af zijn = to be finished

Examples:

• Ik ben af. = I’m finished / done.
• De film is af. = The film is finished.
• Zijn project is nog niet af. = His project isn’t finished yet.

So in Ons huiswerk is al af, af does not mean something like off in a literal physical sense, even though that is one of its meanings in other contexts.

Al here means already.

So:

• Ons huiswerk is af. = Our homework is done.
• Ons huiswerk is al af. = Our homework is already done.

It adds the idea that this happened earlier than expected, or that the speaker is emphasizing that it has been completed.

Examples:

• Ik ben al klaar. = I’m already ready.
• We zijn al thuis. = We’re already home.
• Ben je al klaar? = Are you ready already?

In a simple main clause, Dutch usually puts the finite verb in the second position. That is why is comes right after Ons huiswerk.

Then other sentence parts follow:

• Ons huiswerk = subject
• is = finite verb
• al = adverb
• af = complement/predicate

So the basic order is:

• Subject + verb + other information

That gives:

• Ons huiswerk is al af.

You can also change the emphasis by moving another part to the front:

• Al is ons huiswerk af is not normal as a simple statement.
• Ons huiswerk is af is the neutral version.
• Ons huiswerk is al af adds already in the natural place.

Grammatically, huiswerk is usually treated as a singular uncountable noun, much like homework in English.

So you say:

• het huiswerk
• ons huiswerk is af

Not:

• de huiswerk
• ons huiswerk zijn af

This is similar to English:

• The homework is done, not the homework are done.

Even if the homework contains many exercises, Dutch normally still treats huiswerk as one mass noun.

Yes. That means The homework is already done.

The difference is:

• Het huiswerk = the homework
• Ons huiswerk = our homework

So ons is simply the possessive determiner that tells you whose homework it is.

Compare:

• Het huiswerk is al af. = The homework is already done.
• Jullie huiswerk is al af. = Your homework is already done.
• Hun huiswerk is al af. = Their homework is already done.

Yes, in many contexts you can, and it would sound natural.

Both af and klaar can suggest that something is finished, but there is a slight nuance:

• af often emphasizes that something has been completed
• klaar often means ready or finished

Examples:

• Mijn werk is af. = My work is finished.
• Ik ben klaar. = I’m ready / I’m done.

For homework, both are possible:

• Ons huiswerk is al af.
• Ons huiswerk is al klaar.

But af is especially common when talking about completing a task or piece of work.

In Dutch yes/no questions, the verb usually comes first.

So:

• Ons huiswerk is al af. = Our homework is already done. becomes
• Is ons huiswerk al af? = Is our homework already done?

That is a very common pattern:

• Hij is thuis. → Is hij thuis?
• Het eten is klaar. → Is het eten klaar?

So the sentence structure changes mainly by moving is to the front.