Jeg er vant til at tage metroen til universitetet om morgenen.

It means I am used to ...

The core expression is:

• jeg = I
• er = am
• vant til = used to

So Jeg er vant til at tage metroen means I am used to taking the metro.

A very important point for English speakers:

• at være vant til = to be used to something
• it does not mean the same as English used to in the past-habit sense

So this sentence describes a current state: taking the metro is normal/familiar for the speaker.

Because vant normally goes with til in Danish.

You learn it as a fixed expression:

• at være vant til noget = to be used to something
• at være vant til at gøre noget = to be used to doing something

Examples:

• Jeg er vant til kaffe. = I am used to coffee.
• Jeg er vant til at stå tidligt op. = I am used to getting up early.

So in your sentence, til is not optional. It belongs to the expression vant til.

This is a very common learner question.

In English, after be used to, you normally use a noun or -ing form:

• I am used to the metro
• I am used to taking the metro

In Danish, after vant til, you can have:

• a noun: Jeg er vant til metroen
• or til at + infinitive: Jeg er vant til at tage metroen

So Danish uses:

• til + noun
• or til at + verb

That is just the normal Danish pattern. You should not try to copy the English -ing structure directly.

Yes, tage literally means take, and Danish often uses it for forms of transport, just like English does.

So:

• tage metroen = take the metro
• tage bussen = take the bus
• tage toget = take the train

This is very natural Danish.

You may also hear other transport expressions, depending on context, such as:

• køre med metro = go/travel by metro

But in this sentence, tage metroen is completely normal and idiomatic.

Metroen is the definite form: the metro.

• en metro = a metro
• metroen = the metro

In Danish, when talking about a regular means of transport in a specific, familiar way, the definite form is very common:

• tage bussen
• tage toget
• tage metroen

This works a lot like English:

• take the bus
• take the train
• take the metro

So metroen is natural because it refers to the metro as the known transport system the speaker normally uses.

Because Danish usually uses the definite form here:

• universitetet = the university

English can say go to university without an article, especially in British English, when talking about university as an institution. Danish usually does not do that in the same way.

So Danish normally says things like:

• gå på universitetet = study at university / go to university
• tage til universitetet = go to the university / head to university

For an English speaker, this often feels more definite than the English equivalent, but in Danish it is the normal choice.

Because til shows movement toward a place, while på often shows being at the place.

So:

• til universitetet = to the university
• på universitetet = at the university

In your sentence, the speaker is taking the metro to the university, so the direction matters. That is why til is used.

Compare:

• Jeg tager til universitetet. = I’m going to the university.
• Jeg er på universitetet. = I’m at the university.
• Jeg går på universitetet. = I study at university / I attend university.

Om morgenen means in the morning.

This is a time expression used for something that happens regularly or generally.

• om morgenen = in the morning
• om aftenen = in the evening
• om natten = at night

Do not confuse it with:

• i morgen = tomorrow

That is a completely different expression.

Also, om morgen without -en is not the normal standard form here. The usual expression is om morgenen.

Here is the structure:

• Jeg = I
• er = am
• vant til = used to
• at tage = to take / taking
• metroen = the metro
• til universitetet = to the university
• om morgenen = in the morning

So the full structure is:

Jeg
subject

er
present-tense verb

vant til
predicate/adjective expression

at tage metroen til universitetet om morgenen
infinitive phrase explaining what the person is used to

Inside that infinitive phrase:

• tage = verb
• metroen = object
• til universitetet = direction
• om morgenen = time

No. This is one of the biggest possible misunderstandings.

Jeg er vant til at tage metroen til universitetet om morgenen means:

• I am used to taking the metro to the university in the morning

It describes something that feels normal or familiar now.

If you want I used to take the metro... in the sense of a past habit, Danish would normally use something like:

• Jeg plejede at tage metroen til universitetet om morgenen.

So:

• er vant til = am used to
• plejede at = used to do, in the past

To make it negative, put ikke after the verb er:

• Jeg er ikke vant til at tage metroen til universitetet om morgenen.
• I am not used to taking the metro to the university in the morning.

To make it a yes/no question, invert the subject and verb:

• Er du vant til at tage metroen til universitetet om morgenen?
• Are you used to taking the metro to the university in the morning?

This is standard Danish word order:

• statement: Jeg er ...
• question: Er jeg/du/han ... ?

Yes. A few alternatives are possible depending on style and meaning.

For example:

• Jeg er vant til at tage metro til universitetet om morgenen.
• Jeg er vant til at tage metroen til uni om morgenen.
  More informal, because uni is casual.
• Jeg er vant til at køre med metro til universitetet om morgenen.

These are similar, but not always identical in tone:

• tage metroen sounds very natural and direct
• køre med metro emphasizes traveling by metro
• uni is informal speech, not neutral formal Danish

So the original sentence is a very good standard version.