Han husker kysset.

Because Danish verbs do not change for person.

So:

• jeg husker = I remember
• du husker = you remember
• han husker = he remembers
• vi husker = we remember

English adds -s with he/she/it in the present tense, but Danish uses the same present-tense form for all persons.

The base form is the infinitive at huske = to remember.

The form husker is the present tense. For many Danish verbs, the present tense is made by adding -r:

• at huske → husker
• at komme → kommer
• at læse → læser

So husker is simply the normal present form.

In Danish, the definite article is usually attached to the end of the noun instead of standing in front of it.

So:

• et kys = a kiss
• kysset = the kiss

This is very common in Danish. English says the kiss, but Danish often says, literally, kiss-the.

Here, -et marks the noun as definite singular.

The noun is:

• et kys = a kiss

Since kys is a neuter noun (shown by et), its usual definite singular ending is -et:

• et kys → kysset

So -et here is not a separate word; it is the attached form of the for this noun.

That is a spelling pattern in Danish.

The basic noun is kys, but when an ending is added, the final consonant is often doubled in writing in words of this type:

• kys → kysset

This helps reflect the short vowel before the consonant. So the extra s is a spelling feature, not a separate grammatical ending by itself.

Here it is a noun.

That matters because kysset can also look like the past participle of at kysse = to kiss. But in this sentence, after husker, it functions as the direct object:

• Han husker kysset = he remembers the kiss

So in this sentence, kysset is understood as the kiss, not kissed.

Because han is the subject form of the pronoun.

In this sentence, han is the one doing the action of remembering, so Danish uses han:

• han = he
• ham = him

Compare:

• Han husker kysset = He remembers the kiss
• Jeg ser ham = I see him

So han is correct because it is the subject.

In this sentence, yes: it is basically subject + verb + object:

• Han = subject
• husker = verb
• kysset = object

So the structure is very similar to English.

However, Danish main clauses follow the verb-second rule, which means the finite verb stays in second position if something else comes first:

• I dag husker han kysset = Today he remembers the kiss

So this simple sentence looks like English, but Danish word order becomes more distinctive in other sentence patterns.

You usually put ikke after the finite verb in a main clause:

• Han husker ikke kysset = He does not remember the kiss

So the pattern is:

• Han
  • husker
    • ikke
      • kysset

That placement of ikke is very common in Danish main clauses.

Yes, but it would change the grammar and meaning.

• Han husker kysset = he remembers the kiss
• Han husker et kys = he remembers a kiss

So kysset is definite, while et kys is indefinite. Danish makes that distinction very clearly.