Vinnuverndin er mikilvæg.

It is a compound noun plus the definite article:

• vinnu- = work / labour in a compound form
• vernd = protection
• -in = the (definite article attached to the noun)

So vinnuverndin is literally something like the work-protection, i.e. the occupational safety/protection.

Compounds are very common in Icelandic, much more so than in English.

In Icelandic, the definite article is usually a suffix, not a separate word.

So:

• vinnuvernd = occupational safety / work protection
• vinnuverndin = the occupational safety / the work protection

This is a very common Icelandic pattern:

• bíll = car
• bíllinn = the car

So -in here is not a random ending; it is the definite article.

Because the first part of many Icelandic compounds appears in a special compound form, often related to the genitive or stem form of the noun.

The noun is:

• vinna = work

But in compounds it often becomes:

• vinnu-

So:

• vinna
  • vernd → vinnuvernd

You do not always form compounds by simply sticking the dictionary form of a word in front of another word.

Yes, vinnuvernd is feminine.

You can tell from two things in this sentence:

1. The definite ending -in fits a feminine noun here.
2. The adjective mikilvæg is in the feminine singular form.

So the sentence gives you agreement clues: the noun and adjective match.

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

So:

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

In this sentence, the subject is singular, so Icelandic uses er = is.

Because Icelandic adjectives agree with the noun they describe in gender, number, and case.

Here, vinnuverndin is:

• feminine
• singular
• nominative (because it is the subject)

So the adjective must match that:

• masculine singular: mikilvægur
• feminine singular: mikilvæg
• neuter singular: mikilvægt

That is why the sentence has mikilvæg.

Because mikilvæg is a predicate adjective here, not an adjective directly placed before the noun.

Compare:

• Vinnuverndin er mikilvæg. = The occupational safety is important.
• mikilvæg vinnuvernd = important occupational safety
• mikilvæga vinnuverndin would not be the normal structure here

After vera (to be), Icelandic uses a predicate adjective, and that adjective agrees with the subject but does not take a separate attached article.

In other words, the definiteness is carried by the noun vinnuverndin, not repeated on mikilvæg.

It is in the nominative case.

Why? Because it is the subject of the sentence:

• vinnuverndin = the thing being talked about
• er mikilvæg = is important

Predicate adjectives after vera also normally appear in the nominative, so mikilvæg is nominative too.

Yes. That would usually sound more general:

• Vinnuvernd er mikilvæg. = Occupational safety is important.
• Vinnuverndin er mikilvæg. = The occupational safety is important, or occupational safety (the one we are talking about) is important

In Icelandic, leaving out the article often makes a statement sound more general or abstract. With the article, it can sound more specific or context-based.

Yes. This is a very normal Icelandic sentence pattern:

• Subject + verb + adjective/complement

So:

• Vinnuverndin = subject
• er = verb
• mikilvæg = complement

Icelandic main clauses often follow a verb-second pattern, and this sentence fits that perfectly: the verb er is in the second position.

A few useful pronunciation points:

• Stress usually falls on the first syllable of Icelandic words.
• So you would stress VINNU-verndin and MIKIL-væg.
• er is a short form, roughly like is but of course with Icelandic pronunciation.
• The final g in mikilvæg is not pronounced like a hard English g.

A safe beginner rhythm is:

• VINNU-verndin er MIKIL-væg

Even if your sounds are not perfect yet, getting the first-syllable stress right helps a lot.

Because this is an ordinary sentence, not a title or a proper noun.

So Vinnuverndin is capitalized only because it is the first word in the sentence. Icelandic capitalization rules are broadly similar to English in that respect.