Jeg kommer til universitetet med metroen om morgenen.

Yes, kommer is the present tense of at komme, which often means to come, but in Danish it can also be used in the sense of arrive/get to depending on context.

So Jeg kommer til universitetet can mean something like:

• I come to the university
• I get to the university
• I arrive at the university

In natural English, I get to the university is often the most idiomatic translation in this kind of sentence.

Also, til means to here, showing movement toward a destination.

Because til and på do different jobs.

• til universitetet = to the university
  This shows movement toward the place.
• på universitetet = at the university / at university
  This shows location.

So:

• Jeg kommer til universitetet = I get to the university
• Jeg er på universitetet = I am at the university

A learner often mixes these up because English sometimes uses at and to in ways that feel close, but Danish keeps the distinction very clearly here.

Universitetet is the definite form of universitet.

• et universitet = a university
• universitetet = the university

In Danish, the definite article is usually attached to the end of the noun instead of being a separate word like English the.

So:

• universitet = university
• universitetet = the university

In this sentence, the destination is presented as a specific place, so the definite form is natural.

In Danish, means of transport are very often expressed with med + a noun in the definite form:

• med bussen = by bus
• med toget = by train
• med metroen = by metro

So med metroen is the normal way to say by metro.

To an English speaker, the definite form may feel strange, because English usually says by bus, by train, by metro without the. Danish often prefers the definite form in these transport expressions.

This is a very useful distinction:

• med metroen = by metro
  Focus on the means of transport
• i metroen = in the metro
  Focus on being physically inside it

So in your sentence, med metroen is correct because the point is how the speaker gets to the university.

Compare:

• Jeg kommer til universitetet med metroen. = I get to the university by metro.
• Jeg sidder i metroen. = I am sitting in the metro.

Om morgenen means in the morning.

This expression is commonly used for something that happens generally, regularly, or as part of a routine.

So:

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

In your sentence, it gives the time when this happens.

Because Danish uses different expressions for different meanings:

• om morgenen = in the morning, generally / as a routine
• i morges = this morning
• i morgen = tomorrow

So:

• Jeg kommer til universitetet med metroen om morgenen.
  = I get to the university by metro in the morning.
  This sounds habitual or general.

If you said i morges, it would refer specifically to this morning, not mornings in general.

Also, i morgenen is generally not the normal expression for in the morning in standard Danish.

Most likely it describes a habit or usual way of getting there.

Danish present tense often covers both:

• something happening now
• something that happens regularly

So Jeg kommer til universitetet med metroen om morgenen will usually be understood as:

• I get to the university by metro in the morning
• I go to the university by metro in the morning

Because of om morgenen, it strongly suggests a routine rather than a one-time event happening at this exact moment.

The sentence is natural as written, but Danish word order can be flexible.

Your sentence:

• Jeg kommer til universitetet med metroen om morgenen.

You could also say:

• Om morgenen kommer jeg til universitetet med metroen.

This puts more focus on in the morning.

Both are correct, but the first version sounds like a neutral statement. The second highlights the time expression more.

Yes. In a normal main clause, Danish usually follows subject + verb + other elements.

So:

• Jeg = subject
• kommer = verb

That gives:

• Jeg kommer ...

This is the standard word order for a plain statement.

If another element comes first, then the verb still stays in second position:

• Om morgenen kommer jeg til universitetet med metroen.

This is an important rule in Danish, often called the V2 rule: the verb is in the second position in main clauses.

Yes, absolutely. That is also very natural.

• Jeg kommer til universitetet med metroen om morgenen
  = I get to the university by metro in the morning
• Jeg tager metroen til universitetet om morgenen
  = I take the metro to the university in the morning

The second version focuses more directly on the transport choice: I take the metro.
The original sentence focuses a bit more on arriving/getting there.

Both are good Danish, but tager metroen may sound especially natural in everyday speech when talking about travel habits.