Forbindelsesflyet er klar efter mellemlandingen.

Because Danish normally writes compound nouns as a single word.

So forbindelsesflyet can be broken down like this:

• forbindelse = connection
• s = a linking letter
• fly = plane / aircraft
• -et = the for a neuter noun

A native English speaker often expects something like connection plane as two words, but Danish usually combines this into one compound noun.

The -s- is a linking element. It does not mean possession here.

It is just a very common way of joining parts of a compound in Danish. So forbindelsesfly is not the connection’s plane. It is simply the normal compound form.

You will see this in many other Danish compounds too.

Because the two nouns have different grammatical genders.

• et fly → flyet
• en mellemlanding → mellemlandingen

Danish has two genders:

• common gender: usually takes en / -en
• neuter: usually takes et / -et

Also, in a compound noun, the last part decides the gender. Since fly is a neuter noun, forbindelsesfly is also neuter:

• et forbindelsesfly
• forbindelsesflyet

In Danish, the definite article is usually attached to the end of the noun instead of standing as a separate word.

So:

• flyet = the plane
• mellemlandingen = the stopover

This is one of the biggest differences from English.

A separate word like den/det is mainly used when there is an adjective:

• det næste fly = the next plane
• den lange mellemlanding = the long stopover

Because the sentence refers to a specific stopover, not just any stopover in general.

So mellemlandingen means the stopover. The speaker assumes that this stopover is known from the context.

If it were nonspecific, you would more likely say en mellemlanding.

Here klar means ready, and er klar is the normal idiomatic way to say that something is ready.

So Danish commonly says:

• Flyet er klar
• Maden er klar
• Vi er klar

You will also meet klart in other uses of the adjective, especially when it means clear or obvious, for example:

• Det er klart

So in this sentence, klar is the natural form.

Yes, absolutely. That is also correct Danish.

Danish follows the verb-second rule in main clauses. That means the finite verb must stay in the second position.

So both of these are correct:

• Forbindelsesflyet er klar efter mellemlandingen.
• Efter mellemlandingen er forbindelsesflyet klar.

But this would be wrong:

• Efter mellemlandingen forbindelsesflyet er klar

because the verb er is no longer in second position.

Yes. Danish compounds are often quite literal.

forbindelsesfly is built from the idea of a connection plus a plane/flight. English may choose different natural translations depending on context, such as connecting flight or connecting plane, but the Danish word itself is a straightforward compound.