Við stoppuðum við stóran poll af því að skórnir hennar voru nýir.

They are two different words that just happen to be spelled the same.

• Við at the beginning means we.
• við later in the sentence is a preposition meaning by, at, near.

So Við stoppuðum við stóran poll means We stopped by a big puddle.

Stoppuðum is the past tense, 1st person plural form of stoppa (to stop).

So:

• að stoppa = to stop
• við stoppum = we stop
• við stoppuðum = we stopped

The ending -uðum is a common past-tense ending for we with many weak verbs.

Because the preposition við takes the accusative case.

The noun is pollur (puddle), masculine singular. In the accusative singular, it becomes poll.
The adjective stór (big) has to agree with the noun, so masculine singular accusative is stóran.

So:

• nominative: stór pollur
• accusative: stóran poll

That is why the sentence has við stóran poll.

Here it means by/at a big puddle.

Even though English often makes a strong distinction between movement and location, Icelandic prepositions do not always work in exactly the same way as English ones. With stoppa við, the idea is stop by / stop at something.

So Við stoppuðum við stóran poll is best understood as We stopped by a big puddle.

Af því að is a very common fixed expression meaning because.

It is best learned as a whole phrase, not as three separate words you try to translate one by one every time. Icelandic also has other ways to say because, such as vegna þess að, but af því að is extremely common in everyday language.

So in this sentence:

• af því að skórnir hennar voru nýir = because her shoes were new

In Icelandic, possessives like hennar (her) very often come after the noun.

So the neutral, natural way to say her shoes is:

• skórnir hennar

Putting hennar before the noun is much less common in ordinary usage and can sound marked, contrastive, or more literary depending on context.

Because Icelandic commonly uses the definite noun together with a possessor.

So:

• skór = shoes
• skórnir = the shoes
• skórnir hennar = her shoes

Literally, it looks like the shoes her, but that is a perfectly normal Icelandic structure. English usually does not use the in this situation, but Icelandic often does.

Nýir agrees with skórnir.

The noun skórnir is:

• masculine
• plural
• nominative

So the adjective also has to be masculine plural nominative:

• nýir = new (masculine plural nominative)

Also, this is a predicate adjective after voru (were), so it uses the strong form:
skórnir hennar voru nýir = her shoes were new.

Voru is the 3rd person plural past tense of vera (to be).

Here the subject is skórnir hennar (her shoes), which is plural, so Icelandic uses the plural past form:

• hann var = he was
• þeir voru = they were
• skórnir hennar voru = her shoes were

So voru matches the plural subject.

Yes. After af því að you get a subordinate clause, and the normal order there is subject + verb:

• skórnir hennar = subject
• voru = verb
• nýir = complement

So af því að skórnir hennar voru nýir has a very normal subordinate-clause structure. For learners, the safest approach is simply to remember that after af því að, Icelandic usually looks more like straightforward subject + verb order.