Kan du møde mig kvart over fem ved stationen, eller har du tænkt dig at komme senere?

In Danish, yes/no questions usually begin with the finite verb, just like in English:

• Kan du ...? = Can you ...?
• Har du ...? = Have you ...?

So Kan du møde mig ...? is the normal word order for a question.

Also, kan du here does not only ask about ability. In context, it often works like a polite request: Can you meet me ...?

Because møde normally takes a direct object in Danish:

• Jeg møder dig = I meet you
• Kan du møde mig ...? = Can you meet me ...?

English learners often expect a preposition because English sometimes uses meet with, but plain meet someone matches Danish better here.

A related form is mødes med, which means meet up with each other or meet with:

• Vi mødes ved stationen = We’ll meet at the station
• Jeg skal mødes med ham = I’m meeting him / meeting up with him

Kvart over fem means quarter past five or 5:15.

Danish time expressions commonly use:

• fem over fem = five past five
• kvart over fem = quarter past five
• halv seks = 5:30
• kvart i seks = quarter to six

Be careful with halv seks: in Danish it means halfway to six, so it is 5:30, not 6:30.

Because Danish often omits klokken when the meaning is clear.

So both are possible:

• kvart over fem
• klokken kvart over fem

In everyday speech, leaving out klokken is very common.

Ved often means by, at, or near.

So ved stationen means at/by the station. It suggests the meeting point is in the area of the station, not necessarily inside it.

Compare:

• ved stationen = by/at the station
• på stationen = at the station, often more like on the station premises
• i stationen = in the station building

In this sentence, ved stationen is a very natural choice for a meeting place.

Because Danish usually adds the definite article to the end of the noun.

• en station = a station
• stationen = the station

So instead of putting the before the noun, Danish often uses an ending:

• the station = stationen
• the car = bilen
• the house = huset

It is a very common expression meaning do you intend to, are you planning to, or sometimes are you really going to.

So:

• har du tænkt dig at komme senere? = are you planning to come later?

This is more than just thinking in general. It suggests intention.

Examples:

• Jeg har tænkt mig at rejse i morgen = I’m planning to travel tomorrow
• Hvad har du tænkt dig at gøre? = What are you planning to do?

Yes, basically yes.

Learners should treat at have tænkt sig at + infinitive as a set phrase meaning to intend / to plan to do something.

Structure:

• har = have
• tænkt = thought
• sig = oneself
• at + infinitive

Examples:

• Hun har tænkt sig at blive hjemme = She intends to stay home
• Har du tænkt dig at ringe? = Do you plan to call?

Even though the literal pieces may look strange, the whole expression is idiomatic.

Because after this expression, Danish uses at + infinitive:

• har tænkt sig at komme
• har tænkt sig at vente
• har tænkt sig at sige noget

So komme is in the infinitive form, and at is the infinitive marker, similar to English to.

Yes. Senere is related to sen (late), and here it means later.

In this sentence, it functions adverbially:

• komme senere = come later

Examples:

• Jeg kommer senere = I’m coming later
• Vi kan tale om det senere = We can talk about it later

So even though it comes from a comparative form, you can simply learn senere here as later.

Because the second part is also a question.

The sentence is basically offering two possibilities:

• Can you meet me at 5:15 at the station,
• or are you planning to come later?

Since the second clause is still a yes/no question, Danish keeps question word order:

• har du ...?

If it were a statement, it would be:

• du har tænkt dig ...

But here it is clearly a question, so the verb comes before the subject.

It can be both, depending on context.

Literally, Kan du møde mig ...? means Can you meet me ...?, so it could ask about practical possibility. But in normal conversation it often works as a polite request or arrangement question.

So the speaker is probably asking something like:

• Would you be able to meet me ...?
• Can you meet me ...?

The tone is natural and common in everyday Danish.