Inngangurinn er við torgið, en útgangurinn er bakvið húsið.

Because Icelandic usually puts the definite article the onto the end of the noun instead of using a separate word.

So:

• inngangur = entrance

• inngangurinn = the entrance

• útgangur = exit

• útgangurinn = the exit

• torg = square

• torgið = the square

• hús = house
• húsið = the house

This is one of the first big differences from English.

Because Icelandic nouns have grammatical gender, and the definite article changes form depending on gender and case.

In this sentence:

• inngangur and útgangur are masculine
• torg and hús are neuter

That is why the definite forms look different:

• masculine: inngangurinn, útgangurinn
• neuter: torgið, húsið

So the ending is not random; it reflects the noun’s grammar.

No. In this sentence, við is a preposition, not the pronoun we.

Here it means something like:

• by
• near
• next to

So við torgið means by the square or near the square.

Icelandic has several words that are spelled the same but have different functions depending on context. Here, the position in the sentence makes it clear that við is a preposition.

They are both place expressions, but they describe different locations.

• við torgið = by / near the square
• bakvið húsið = behind the house

So:

• við gives the idea of being close to something
• bakvið gives the idea of being at the back of something

They are both answering the question where?

Because prepositions in Icelandic control case.

In this sentence:

• við takes the accusative
• bakvið also takes the accusative

So torgið and húsið are accusative forms here.

A useful thing to know is that for many neuter singular nouns, the nominative and accusative look the same. That means you do not see a visible change here, even though the case is accusative.

So the grammar is changing, but the form happens to stay the same.

Because this sentence has two full clauses joined by en.

• Inngangurinn er við torgið
• en útgangurinn er bakvið húsið

Each clause needs its own verb, and er is the singular present form of vera = to be.

So Icelandic works like English here:

• The entrance is by the square, but the exit is behind the house.

You would not normally leave out the second er.

Because each subject is singular:

• inngangurinn = the entrance = singular
• útgangurinn = the exit = singular

So each clause takes singular er.

You would use eru only with a plural subject, for example:

• Inngangarnir eru... = The entrances are...

En means but.

It is a coordinating conjunction used to connect two clauses and show contrast:

• the entrance is in one place
• but the exit is in another place

So it works very much like English but in this sentence.

The sentence as given is very natural, but Icelandic word order is somewhat flexible.

The basic order here is:

• subject + verb + place expression

So:

• Inngangurinn er við torgið
• útgangurinn er bakvið húsið

You can also move the place expression to the front for emphasis, for example:

• Við torgið er inngangurinn...

That kind of change is possible, but the verb still follows Icelandic word-order rules, especially the tendency for the finite verb to stay early in the clause.

So yes, the order can change, but not freely in every direction.

Yes. They are closely related compound nouns.

Both contain gangur, which is connected with going, walking, or passage.

• inn- = in
• út- = out
• gangur = passage / going

So:

• inngangur is literally something like in-going / entrance
• útgangur is literally something like out-going / exit

This is very common in Icelandic: long words are often built from smaller meaningful parts.

Because við torgið and á torginu do not mean exactly the same thing.

• við torgið = by the square / near the square
• á torginu = in the square / on the square itself

So við torgið places the entrance next to the square rather than inside the square area.

This is a good example of how Icelandic prepositions often express location quite precisely.