Grenndarstöðin er nálægt.

Because Icelandic makes very heavy use of compound nouns. What English often writes as two words or with of, Icelandic often packs into one word.

Here, Grenndarstöðin is built from:

• grenndar- = related to grennd (vicinity, neighborhood)
• stöð = station

So the whole word is literally something like the neighborhood station. In real usage, this often refers to a local drop-off or recycling station.

The -in is the definite article, meaning the.

In Icelandic, the is usually added to the end of the noun instead of standing as a separate word.

So:

• grenndarstöð = a neighborhood station / recycling station
• grenndarstöðin = the neighborhood station / the recycling station

That is one of the first big differences English speakers notice in Icelandic.

It is:

• feminine
• singular
• nominative

Why?

• stöð is a feminine noun
• there is only one station here, so it is singular
• it is the subject of the sentence, so it is in the nominative

That is why the definite ending appears in the form it does.

Er is the present tense, third-person singular form of að vera (to be).

So:

• ég er = I am
• þú ert = you are
• hann/hún/það er = he/she/it is

Since Grenndarstöðin is a singular subject, Icelandic uses er:
Grenndarstöðin er nálægt. = The recycling center is nearby.

That is a very good question, because learners often expect adjective agreement here.

In this sentence, nálægt is being used adverbially, meaning something like nearby or close by, rather than as a normal agreeing adjective. Because of that, it does not change to match the feminine noun.

So:

• Grenndarstöðin er nálægt. = The recycling center is nearby.

If you are thinking in terms of agreement, that instinct is reasonable, but this sentence uses the fixed form nálægt.

Yes. Nálægt can also be used with a following noun, and that noun goes in the dative.

For example:

• Grenndarstöðin er nálægt skólanum.
• The recycling center is close to the school.

Here:

• skólinn = the school (nominative)
• skólanum = the school in the dative

So a very useful pattern is:

X er nálægt + dative noun

No, this is the normal, neutral word order for a simple statement:

subject + verb + complement/adverbial

So:

• Grenndarstöðin = subject
• er = verb
• nálægt = complement/adverbial

This is the most straightforward way to say it.

Because in English, if you do not say what something is close to, nearby often sounds more natural.

So:

• Grenndarstöðin er nálægt. can mean The recycling center is nearby
• It can also be understood as The recycling center is close

But English usually prefers:

• close to + something
• or simply nearby if no comparison point is stated

So the Icelandic sentence can stand on its own very naturally, while English often chooses nearby to sound smoother.