Noget affald skal i den grå pose, men metal og glas skal sorteres for sig.

Because affald is normally an uncountable noun, like waste or trash in English.

• noget is used with uncountable nouns: noget affald = some waste
• nogle is used with countable plural nouns: nogle poser = some bags

So noget affald is the natural choice here.

Danish often leaves out a verb of placement when the meaning is obvious.

So skal i den grå pose is a shortened, natural way of saying something like:

• skal lægges i den grå pose
• skal puttes i den grå pose

English usually needs the extra verb, but Danish can be more compact here.

When a Danish noun is definite and has an adjective before it, Danish normally uses this pattern:

• den/det/de + adjective + noun in basic form

So:

• posen = the bag
• den grå pose = the grey bag

You do not usually combine den with posen in standard Danish here.

Because grå is one of the adjectives that usually stays the same in forms like this.

Compare:

• en grå pose
• den grå pose
• grå poser

But in neuter singular, it does change:

• et gråt låg

So grå does inflect, but not in every form.

Here skal mainly expresses obligation, rule, or instruction, not simple future.

In this kind of notice or instruction, skal is close to:

• must
• is to
• sometimes should, depending on tone

So the sentence is giving a rule about how the waste must be sorted.

Because sorteres is the passive form.

• sortere = to sort
• sorteres = to be sorted

So:

• metal og glas skal sorteres = metal and glass must be sorted

If you used skal sortere, it would mean metal and glass must sort, which does not fit the meaning.

For sig is an idiomatic expression meaning separately or apart.

So skal sorteres for sig means that metal and glass should be kept separate in the sorting process.

It is best not to translate sig too literally here. The whole phrase for sig works as a set expression.

Because metal and glas are being used as general material categories, not as specific individual items.

This is similar to English:

• Metal and glass must be sorted
• not necessarily the metal and the glass

Danish often leaves out the article when talking about things in a general way.

Because men is a coordinating conjunction. It joins two main clauses, and the second clause keeps normal main-clause word order:

• metal og glas = subject
• skal = verb

So:

• ..., men metal og glas skal sorteres for sig

There is no inversion just because of men.

Because the sentence has two main clauses joined by men:

• Noget affald skal i den grå pose
• metal og glas skal sorteres for sig

In Danish, a comma before men is standard in this kind of sentence. It helps show the boundary between the two clauses.