Hún flokkar plastumbúðirnar og glerumbúðirnar meðan við berum málminn.

Because Icelandic very often forms compound nouns as one word.

• plast + umbúðirnar → plastumbúðirnar
• gler + umbúðirnar → glerumbúðirnar

The last part, umbúðir, is the main noun, and the first part tells you what kind of packaging it is: plastic packaging, glass packaging.

A useful rule:

• In Icelandic compounds, the last element is the grammatical head.
• So the whole word behaves like umbúðir in gender, number, and inflection.

That is a very common point of confusion. Umbúðir is normally a plural noun in Icelandic. It often means packaging, wrappings, or containers/packing material.

So even when English uses singular packaging, Icelandic often uses plural umbúðir.

That means:

• plastumbúðirnar = the plastic packaging
• glerumbúðirnar = the glass packaging

So the plural form does not necessarily mean several separate packages in the English sense. It is just how Icelandic commonly expresses this idea.

The ending -nar is the suffixed definite article: it means the.

Icelandic usually attaches the to the end of the noun instead of using a separate word.

So:

• umbúðir = packaging / wrappings
• umbúðirnar = the packaging / the wrappings

Because plastumbúðirnar and glerumbúðirnar are feminine plural definite forms, they end in -nar.

Because málmur and umbúðir are different kinds of nouns.

• umbúðir is feminine plural
• málmur is masculine singular

So their definite endings are different:

• umbúðirnar = the packaging
• málminn = the metal

Here is the pattern:

• málmur = metal
• málminn = the metal

So -inn is the definite ending for this masculine singular form.

They are in the accusative, because they are direct objects of the verbs.

In the sentence:

• Hún flokkar plastumbúðirnar og glerumbúðirnar
  • she sorts the plastic packaging and the glass packaging
• við berum málminn
  • we carry the metal

The direct objects are:

• plastumbúðirnar
• glerumbúðirnar
• málminn

Those verbs commonly take the accusative:

• að flokka eitthvað = to sort something
• að bera eitthvað = to carry something

A small extra note:

• For umbúðirnar, nominative and accusative plural look the same.
• For málminn, the accusative form is visible in the form you see.

They are present-tense forms of two different verbs:

• flokkar ← að flokka = to sort
• berum ← að bera = to carry

In this sentence:

• hún flokkar = she sorts
• við berum = we carry

So the structure is:

• Hún flokkar ...
• meðan við berum ...

This is very normal Icelandic present-tense usage.

Because Icelandic verbs change form depending on the subject.

For að bera in the present tense, some forms are:

• ég ber = I carry
• þú berð = you carry
• hann/hún/það ber = he/she/it carries
• við berum = we carry

So with við = we, the correct form is berum.

This is just ordinary subject-verb agreement.

Meðan means while or during the time that. It introduces a subordinate clause.

So:

• meðan við berum málminn = while we carry the metal

It links the two actions as happening at the same time:

• she is sorting
• while we are carrying the metal

So meðan is functioning as a conjunction, much like English while.

Not in the way learners sometimes expect from languages where subordinate clauses force the verb to the end. In Icelandic, the clause after meðan can still look quite straightforward:

• meðan við berum málminn

That is simply:

• við = subject
• berum = finite verb
• málminn = object

So the subordinate clause keeps a very natural order here.

In Icelandic, málmur can be used as a material or category word, much like English metal.

So málminn here means something like:

• the metal
• the metal recycling
• the metal material/items in that category

Even if several metal objects are involved in real life, the singular can still be natural when talking about the category as a whole.

If you wanted to emphasize multiple separate metal objects, a plural form could be used in another context, but the singular here is perfectly normal.

Yes. You could say:

• Meðan við berum málminn, flokkar hún plastumbúðirnar og glerumbúðirnar.

That means the same thing.

But notice the main clause word order after the initial subordinate clause:

• flokkar hún not
• hún flokkar

This happens because Icelandic is generally a verb-second language in main clauses. When the sentence begins with Meðan við berum málminn, that whole subordinate clause takes the first slot, so the finite verb of the main clause comes next.

Because they are two separate definite noun phrases joined by og = and.

So Icelandic says, literally:

• the plastic packaging and the glass packaging

with definiteness marked on both nouns:

• plastumbúðirnar
• glerumbúðirnar

That is completely normal. Icelandic does not usually make one article cover both nouns in the way English sometimes can.