Min søster glæder sig til fredag, fordi hun har fridag.

Min is a possessive adjective meaning my, and søster means sister.

So min søster = my sister.

You would only use søsters if sister itself were possessive, for example:

• min søsters bil = my sister’s car

So in your sentence, min is the word showing possession, not søster.

Because at glæde sig til is a reflexive expression in Danish. The verb normally appears with a reflexive pronoun when it means to look forward to.

So:

• jeg glæder mig
• du glæder dig
• han/hun glæder sig
• vi glæder os
• I glæder jer
• de glæder sig

In this sentence, sig matches hun.

A useful way to learn it is as a whole chunk:

• at glæde sig til noget = to look forward to something

So don’t think of glæder alone here; think of glæder sig til as one pattern.

Sig is the reflexive pronoun used for himself/herself/itself/themselves in the third person.

In this sentence:

• hun glæder sig = she looks forward
  literally something like she gladdens herself, though that literal idea is not how you should translate it in normal English

The important point is that Danish requires the reflexive pronoun in this expression.

Compare:

• Jeg glæder mig
• Hun glæder sig
• De glæder sig

After glæde sig, Danish uses til:

• glæde sig til noget = look forward to something

So:

• glæder sig til fredag = looks forward to Friday

This is just the preposition required by the expression. It is best memorized together:

• at glæde sig til

Some more examples:

• Jeg glæder mig til ferien = I’m looking forward to the holiday
• Vi glæder os til weekenden = We’re looking forward to the weekend

When Danish refers to a day of the week in this kind of general time expression, it normally does not use an article.

So:

• til fredag = to / for Friday
• på fredag = on Friday
• mandag, tirsdag, fredag etc. usually appear without en/et

Also, days of the week in Danish are normally not capitalized, unlike in English:

• fredag, not Fredag

They are related, but they are used differently.

• glæde sig til fredag = look forward to Friday
• på fredag = on Friday

So:

• Min søster glæder sig til fredag = she is looking forward to Friday
• Hun har fridag på fredag = she has the day off on Friday

Til belongs with glæde sig til.
På is used when stating that something happens on that day.

Because fordi introduces a subordinate clause, and subordinate clauses normally keep the order subject + verb.

So:

• fordi hun har fridag

Here:

• hun = subject
• har = verb
• fridag = object/complement

This is normal Danish clause structure after fordi.

A very useful thing to remember is that in subordinate clauses, words like ikke usually come before the finite verb:

• fordi hun ikke har fridag

That helps learners recognize subordinate-clause word order.

Both are present tense:

• glæder = present tense of glæde
• har = present tense of have

Danish often uses the present tense for something happening now or for something connected to the near future, especially when the time is clear from context.

So here, the meaning is basically that she is looking forward to Friday, and Friday is of course still in the future.

Fridag is a compound noun:

• fri = free / off
• dag = day

Together:

• fridag = day off

Danish very often forms new nouns by joining words together into one word, much more than English does.

Examples:

• sommerferie = summer holiday
• arbejdsdag = workday
• fødselsdag = birthday

So fridag as one word is completely normal Danish spelling.

In this sentence, have fridag is an idiomatic expression meaning to have the day off / be off work or school.

So Danish often says:

• Jeg har fridag i morgen = I have the day off tomorrow

Using en is possible in some contexts, but it changes the feel. Har fridag sounds like a general state or schedule fact: she is off that day.

So in your sentence, har fridag is the most natural choice.

Yes. At se frem til is another common way to say to look forward to.

So these are both natural:

• Min søster glæder sig til fredag
• Min søster ser frem til fredag

There can be a slight stylistic difference:

• glæde sig til often feels very common, everyday, and personal
• se frem til can sound slightly more neutral or sometimes a bit more formal, depending on context

But in many situations, both work well.

A rough guide for an English speaker:

• søster: the sø sound does not exist in English; it is something like a rounded vowel, a bit like saying sir while rounding your lips
• glæder: the æ is like the vowel in cat, but often a bit more open
• sig: in standard Danish, it often sounds more like sai than a hard English sig

Very rough approximations:

• søster ≈ SUR-ster with rounded lips on the first vowel
• glæder sig ≈ GLEH-ther sai

These are only approximations. Danish pronunciation varies a lot from spelling, so it is especially helpful to hear native audio for this sentence.

Yes. Danish main clauses normally follow the V2 rule, which means the finite verb is in the second position.

Here the clause begins with the subject:

• Min søster | glæder | sig til fredag

So the verb glæder is in second position.

If you move another element to the front, the verb still stays second:

• Til fredag glæder min søster sig

That sounds more marked, but it shows the same rule. This is a very important pattern in Danish main clauses.