I marts har min far fødselsdag, og i oktober har min mor fødselsdag.

In Danish, i is the normal preposition for months when you mean in a particular month.

• i marts = in March
• i oktober = in October

This is very similar to English in March and in October. You would not normally use på here.

Both are correct, but the word order changes because Danish follows the verb-second rule in main clauses.

If you start with a time phrase like I marts, the finite verb must come next:

• I marts har min far fødselsdag.

If you start with the subject, then the verb still comes second:

• Min far har fødselsdag i marts.

So the sentence you were given puts focus on the time: In March...

This is the Danish V2 rule: in a main clause, the conjugated verb usually comes in the second position.

So the structure is:

• I marts = first element
• har = second element, the finite verb
• min far = subject
• fødselsdag = rest of the clause

English learners often expect the subject to come right after the time expression, but Danish often puts the verb there instead.

Literally, har fødselsdag means has birthday.

This is the normal Danish expression for saying that it is someone’s birthday. English usually says:

• My father has a birthday in March or more naturally:
• My father’s birthday is in March

But Danish uses the verb have here:

• min far har fødselsdag
• min mor har fødselsdag

Because have birthday is an idiomatic expression in Danish. You normally say:

• have fødselsdag = to have a birthday

You do not usually say have en fødselsdag in this meaning.

So:

• Min far har fødselsdag i marts. = correct
• Min far har en fødselsdag i marts. = unnatural for this meaning

In Danish, possessives like min, din, hans, hendes, and so on usually replace the article.

So you say:

• min far = my father
• min mor = my mother

Not:

• den min far
• en min mor

This works much like English, where you also say my father, not the my father.

Not naturally in this sentence. Danish normally repeats it:

• I marts har min far fødselsdag, og i oktober har min mor fødselsdag.

That sounds complete and natural. Omitting fødselsdag would make the sentence feel incomplete or force a different wording.

If you really wanted to avoid repetition, you would usually rephrase the sentence rather than just drop the word.

Because in Danish, the names of months are normally written with lowercase letters:

• marts
• oktober
• januar
• december

This is different from English, where month names are capitalized.

In your sentence, I is capitalized only because it is the first word of the sentence, not because month names take capitals.

Og means and. It connects the two main clauses:

• I marts har min far fødselsdag
• og i oktober har min mor fødselsdag

So the sentence is really two full statements joined together by og.

Yes. Danish very often combines nouns into one word, and fødselsdag is a compound noun:

• fødsel = birth
• dag = day

Together:

• fødselsdag = birthday

This is very common in Danish, so learners should get used to seeing long single-word nouns.