Læreren spørger, om "kommer" står i nutid, og om "kom" står i datid.

Because -en is the usual Danish definite article attached to the end of a common-gender noun.

• en lærer = a teacher
• læreren = the teacher

So Læreren spørger means The teacher asks.

Here om means whether.

So:

• spørger, om ... = asks whether ...

That is different from other common meanings of om, such as about or around/in depending on context. In this sentence, it definitely means whether.

Because the sentence is talking about the words themselves, not using them normally in a sentence.

So kommer and kom are being mentioned as word forms. In English, we do the same thing:

• The teacher asks whether comes is in the present tense and whether came is in the past tense.

In other words, the Danish sentence is doing grammar talk: it is discussing verb forms as objects of discussion.

Yes, står literally means stands, but in Danish it is also used in grammar talk to mean something like:

• is written as
• appears as
• is in

So:

• står i nutid = is in the present tense
• står i datid = is in the past tense

This is a normal Danish way to talk about grammatical forms.

They are Danish grammar terms:

• nutid = present tense
• datid = past tense

A useful note: in more formal grammar language, you may also see:

• præsens = present tense
• præteritum = past tense / preterite

But nutid and datid are very common and learner-friendly terms.

They are two forms of the verb komme (to come):

• komme = infinitive
• kommer = present tense
• kom = past tense

So the sentence is asking whether the learner can identify those two verb forms correctly.

Because kommer is the subject of that clause — it is the word being discussed — and står is the verb.

The structure is basically:

• om [kommer] [står] i nutid
• whether [comes] [is] in the present tense

So Danish is treating kommer almost like a noun or label here: the form kommer is the thing that står i nutid.

Because there are two parallel subordinate clauses:

• om kommer står i nutid
• om kom står i datid

Repeating om makes the structure clearer and more balanced. English often does the same:

• The teacher asks whether comes is present tense, and whether came is past tense.

You might sometimes see less repetition in other contexts, but here repeating om is very natural.

In Danish, after i in this kind of grammar expression, you usually do not use an article.

So Danish says:

• stå i nutid
• stå i datid

where English says:

• be in the present tense
• be in the past tense

This is just a normal difference between the two languages.

Because om introduces subordinate clauses, and Danish often uses commas before subordinate clauses.

So the sentence is divided like this:

• Læreren spørger, om ... , og om ...

This may look a bit heavier than English punctuation, but it is normal in Danish writing.

Both spørger and står are in the present tense.

• spørger = asks / is asking
• står = stands / is / appears

That can feel a little strange at first, because the sentence also contains kom, which is a past-tense form. But the sentence itself is happening in the present: the teacher asks now about whether one word form is present tense and another is past tense.

No, not in standard Danish for this meaning.

After a verb like spørge when you mean whether, Danish uses om:

• Han spørger, om det er rigtigt. = He asks whether it is correct.

Hvis usually means if in a conditional sense:

• Hvis det regner, bliver vi hjemme. = If it rains, we stay home.

So in this sentence, om is the correct word.