Salernið er til vinstri við innganginn.

It is made of:

• salerni = restroom / toilet
• -ið = the definite article ending for a neuter singular noun, meaning the

So salernið means the restroom or the toilet.

In Icelandic, the definite article is usually added to the end of the noun as a suffix.

For example:

• salerni = restroom
• salernið = the restroom

This is very normal in Icelandic. English uses a separate word (the), but Icelandic usually builds it into the noun.

Er means is. It is the 3rd person singular present form of vera, which means to be.

So:

• salernið er ... = the restroom is ...

Yes, you need er here, just as you need is in English.

Til vinstri is a very common fixed expression meaning to the left or on the left.

Even though til often means to in other contexts, here you should learn til vinstri as a whole phrase. It does not have to be translated word-for-word.

A useful pair is:

• til vinstri = to/on the left
• til hægri = to/on the right

It can do both.

For example:

• Beygðu til vinstri. = Turn left.
• Húsið er til vinstri. = The house is on the left.

So in your sentence, til vinstri is describing location, not movement.

Because Icelandic normally uses the full expression til vinstri when talking about left/right position or direction.

So a beginner should usually memorize:

• til vinstri = to/on the left
• til hægri = to/on the right

Vinstri can appear in other kinds of expressions too, but in a sentence like this, til vinstri is the natural form.

Við innganginn means by the entrance, at the entrance, or near the entrance.

Here:

• við = by / at / near
• innganginn = the entrance

So the sentence is locating the restroom as being on the left, near or by the entrance.

Because við takes the accusative case, and innganginn is the accusative definite singular form.

The noun is:

• inngangur = entrance

Its definite singular forms include:

• inngangurinn = the entrance in the nominative
• innganginn = the entrance in the accusative

Since the preposition við is used here, Icelandic uses innganginn.

Sometimes yes, but it is not exactly the same structure.

• við innganginn = by/at the entrance
• hjá innganginum = also something like by/near the entrance, but with a different preposition and a different case

A key grammar point:

• við takes the accusative
• hjá takes the dative

So:

• við innganginn
• hjá innganginum

In this sentence, við innganginn is very natural and idiomatic.

Yes, but it sounds a bit neutral or formal. It is very common on signs and in public places.

In everyday speech, many people also say:

• klósett = toilet
• sometimes baðherbergi = bathroom, depending on context

So salerni is a perfectly good word, especially in public or polite usage.

Yes. Icelandic word order is somewhat flexible.

The original sentence is:

• Salernið er til vinstri við innganginn.

You could also say:

• Við innganginn er salernið til vinstri.

That change puts more focus on by the entrance. Notice that the verb er still stays in second position. That is a very important Icelandic pattern.

You would say:

• Salernið er til hægri við innganginn.

So the useful pair is:

• til vinstri = to/on the left
• til hægri = to/on the right