Við skulum skoða samninginn aftur á morgun.

It is the normal Icelandic way to say let's when you are including yourself and at least one other person.

So Við skulum ... means Let’s ...

Literally, skulum comes from the verb skulu, which often has meanings related to shall / should / will, but in this pattern it works as an exhortation or suggestion:

• Við skulum fara. = Let’s go.
• Við skulum skoða ... = Let’s look at / review ...

Yes. Skulum is the 1st person plural present form of skulu.

That is why it matches við = we.

In this sentence, though, it is not really best understood as a literal we shall. It is the standard idiomatic construction for making a suggestion:

• Við skulum ... = Let’s ...

Because after skulum, Icelandic uses the infinitive of the main verb.

So:

• skulum skoða not
• skulum skoðum

This is similar to how English uses a base verb after let’s:

• Let’s look not
• Let’s looking

Also, there is no að here. After modal-like verbs such as skulu, the following verb is normally just the bare infinitive.

Because Icelandic does not normally use a simple 1st-person plural imperative the way English uses let’s.

Instead, Icelandic uses:

• Við skulum + infinitive

So if you want to say Let’s review the contract, the natural structure is:

• Við skulum skoða samninginn.

This is because Icelandic main clauses usually follow the V2 rule: the finite verb tends to come in second position.

Here the first element is Við, so the finite verb skulum comes second:

• Við | skulum | skoða samninginn aftur á morgun.

If you start with a different element, the verb still tends to stay second:

• Á morgun skulum við skoða samninginn aftur.

That word order is very typical of Icelandic.

Because samninginn is the direct object of skoða, and skoða takes the accusative.

The basic dictionary form is:

• samningur = contract / agreement
  (nominative singular, indefinite)

But in this sentence you need:

• accusative singular: samning
• accusative singular definite: samninginn

So:

• samningur = a contract as subject form
• samninginn = the contract as object form here

It is the suffixed definite article.

In Icelandic, the is often attached to the end of the noun instead of being a separate word.

So:

• samningur = a contract
• samningurinn = the contract (nominative)
• samninginn = the contract (accusative)

This sentence needs the accusative form, so you get samninginn.

No. Skoða can mean:

• look at
• examine
• inspect
• check
• review

With something like samningur (contract/agreement), it often feels closer to review or go over than just physically looking at it.

So even if the meaning shown to the learner is look at, the Icelandic verb can sound a bit broader than that.

Here aftur means again.

This word can also mean back, depending on context. For example:

• Hann kom aftur. can mean He came back.
• Lesum þetta aftur. means Let’s read this again.

In your sentence, the intended meaning is clearly again: reviewing the contract one more time.

Because á morgun is a fixed Icelandic expression meaning tomorrow.

This can confuse English speakers, because it looks like it might mean something more literal such as on morning, but it does not. It simply means tomorrow.

A very useful contrast is:

• á morgun = tomorrow
• í morgun = this morning

Those two are easy to mix up, so they are worth memorizing as whole expressions.

That is a natural neutral order in Icelandic.

• aftur modifies the action and means again
• á morgun gives the time: tomorrow

So the sentence first says that the action will be repeated, and then adds when:

• skoða samninginn aftur á morgun

You may also hear different word orders for emphasis, but this version is very normal and natural.

A few parts may be difficult for English speakers:

• við: the ð is like the th in this, though at the end of a word it may sound quite weak
• skulum: stress the first syllable: SKU-lum
• samninginn: also stress the first syllable: SAM-ning-inn
• morgun: stress the first syllable: MOR-gun

A good general rule is that Icelandic words are usually stressed on the first syllable.