Plastumbúðirnar eru tómar.

It is a compound noun plus the definite article:

• plast = plastic
• umbúðir = packaging / wrappings / containers
• -nar = the for a feminine plural noun

So plastumbúðirnar literally breaks down as the plastic packaging or the plastic containers/wrappings, depending on context.

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

Here:

• plastumbúðir = plastic packaging / plastic wrappings
• plastumbúðirnar = the plastic packaging / wrappings

The ending -nar is the definite article used here with a feminine plural noun in the nominative.

Yes, umbúðir is plural, and it is very often used in the plural when talking about packaging or wrappings in a general sense.

A singular form umbúð does exist, but it usually refers to a single wrapper, package, or covering. In everyday usage, when people mean packaging, the plural umbúðir is very common.

Because the subject is plural.

The verb vera = to be changes form depending on number:

• er = is
• eru = are

Since plastumbúðirnar is plural, Icelandic uses eru: Plastumbúðirnar eru ...

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

The dictionary form tómur is masculine singular nominative. But plastumbúðirnar is feminine plural, so the adjective must also be feminine plural:

• masculine singular: tómur
• feminine singular: tóm
• neuter singular: tómt
• feminine plural: tómar

So Plastumbúðirnar eru tómar is the grammatically correct agreement.

Because here tómar is a predicate adjective, not an adjective inside the noun phrase.

In other words:

• Plastumbúðirnar eru tómar = The plastic packages are empty.
• tómar plastumbúðir = empty plastic packages

In the sentence you were given, the structure is subject + verb + predicate adjective.

Yes. That would mean Plastic packages/packaging are empty without the definite sense of the.

So the difference is:

• Plastumbúðirnar eru tómar = The plastic packages are empty.
• Plastumbúðir eru tómar = Plastic packages are empty.

That is the same definite vs. indefinite distinction as in many other Icelandic nouns.

It is in the nominative, because it is the subject of the sentence.

A basic Icelandic sentence with vera often looks like this:

• subject in the nominative
• verb
• predicate adjective agreeing with the subject

So plastumbúðirnar is nominative plural, and tómar matches it.

A rough learner-friendly version would be:

PLAS-tum-boo-thir-nar EH-ru TOH-mar

A few notes:

• ú is a long oo sound.
• ð is like the th in this, though it can be softer in real speech.
• r is usually tapped or rolled lightly.
• ó is a long o sound.

This is only an approximation, but it is a useful starting point.