Papaffaldet er tørt.

Because Danish normally writes compound nouns as a single word.

Here:

• pap
  • affald = papaffald

The first part narrows the meaning of the second part. English often uses separate words, but Danish usually joins them:

• paper waste → papaffald
• school bus → skolebus

So papaffaldet is not unusual at all; it is standard Danish spelling.

-et is the definite article attached to the end of the noun.

So:

• papaffald = paper/cardboard waste
• papaffaldet = the paper/cardboard waste

Unlike English, Danish often puts the at the end of the noun instead of using a separate word.

That is one of the basic patterns of Danish.

In many simple cases, Danish uses an enclitic definite article, which means the article is added as a suffix:

• en bil = a car
• bilen = the car
• et hus = a house
• huset = the house

So papaffaldet follows the same pattern.

Er is the present tense of at være, meaning to be.

So Papaffaldet er tørt is a present-tense statement describing a current state.

A useful thing for English speakers: Danish does not change this form for different persons in the present tense:

• jeg er
• du er
• han er
• vi er

It is always er.

Because the adjective has to agree with a neuter singular noun.

The base form is tør, but with a neuter singular noun it becomes tørt.

Compare:

• en avis er tør = a newspaper is dry
• et brev er tørt = a letter is dry

Here, papaffaldet is treated as a neuter noun, so the adjective becomes tørt.

In Danish compounds, the grammatical gender usually comes from the last part of the compound.

So in papaffald:

• the head word is affald
• that determines the gender
• therefore the whole compound behaves like a neuter noun

That is why you get:

• papaffaldet
• tørt

It is an adjective.

It comes after er and describes the noun papaffaldet. That is called a predicative adjective.

So the structure is:

• papaffaldet = subject
• er = verb
• tørt = adjective describing the subject

Even though some Danish adverbs look similar to adjective forms, here tørt is clearly an adjective.

In this simple sentence, yes. It is:

• subject + verb + complement
• Papaffaldet + er + tørt

So it matches English very closely.

However, Danish is a verb-second language in main clauses. That means if you move something else to the front, the verb still stays in second position:

• I dag er papaffaldet tørt = Today the paper/cardboard waste is dry

So the simple sentence looks English-like, but Danish word order has its own rules.

Yes, but the meaning changes slightly.

• Papaffaldet er tørt = the paper/cardboard waste is dry
• Papaffald er tørt = paper/cardboard waste is dry, or paper/cardboard waste in general is dry

So adding -et makes it more specific.

To make it a question, invert the subject and verb:

• Er papaffaldet tørt? = Is the paper/cardboard waste dry?

To make it negative, add ikke:

• Papaffaldet er ikke tørt. = The paper/cardboard waste is not dry.

In a simple main clause, ikke usually comes after the finite verb.