Hvis min niece scorer først, bliver hele holdet glad.

Hvis means if and introduces a condition.

So Hvis min niece scorer først ... means If my niece scores first ...

This is a very common pattern in Danish:

• Hvis
  • condition
• main clause after it

Example:

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

Danish often uses the present tense to talk about a future situation, especially in if-clauses.

So:

• Hvis min niece scorer først literally uses present tense
• but the meaning is future: If my niece scores first

English does something similar in the if-clause:

• If she scores first... not If she will score first...

The main clause also uses present tense in Danish:

• bliver hele holdet glad even though in English you might naturally say the whole team will be happy.

Yes. Danish has borrowed at score from English, especially in sports.

Here:

• at score = to score
• scorer = scores / is scoring

The -r is the normal present-tense ending for many Danish verbs.

So:

• jeg scorer = I score
• hun scorer = she scores

Because the first part is a subordinate clause introduced by hvis, and Danish normally separates that from the main clause with a comma.

So the structure is:

• Hvis min niece scorer først, = subordinate clause
• bliver hele holdet glad. = main clause

That comma is standard Danish punctuation.

This is because Danish follows the verb-second rule in main clauses.

When the sentence starts with something other than the subject—here, the whole if-clause comes first—the finite verb of the main clause must come next.

So:

• Hvis min niece scorer først, bliver hele holdet glad.

Not:

• Hvis min niece scorer først, hele holdet bliver glad.

You can think of it like this:

1. something comes first: Hvis min niece scorer først
2. then the finite verb: bliver
3. then the subject: hele holdet

This is one of the most important Danish word-order patterns to learn.

Bliver means becomes / gets / will be, while er means is.

So:

• hele holdet bliver glad = the whole team becomes happy / gets happy
• hele holdet er glad = the whole team is happy

In this sentence, the happiness happens as a result of the niece scoring first, so bliver is the natural choice.

Holdet is:

• hold = team
• -et = the definite ending

So holdet means the team.

Unlike English, Danish often puts the at the end of the noun:

• en bil = a car
• bilen = the car
• et hold = a team
• holdet = the team

Because holdet already contains the idea of the.

• hold = team
• holdet = the team

And hele means whole / entire, so:

• hele holdet = the whole team

This is the normal Danish way to say it.

Min means my, and it agrees with the gender/number of the noun being possessed.

Since niece is a common-gender singular noun, you use min:

• min niece = my niece

Compare:

• min bil = my car
• mit hus = my house
• mine venner = my friends

So the pattern is:

• min
  • common gender singular
• mit
  • neuter singular
• mine
  • plural

No, not exactly.

Although it is spelled the same, the Danish pronunciation is different. A rough English-friendly approximation is:

• NEE-suh

The last syllable is lightly pronounced, not like the English one-syllable niece.

So this is one of those words that looks familiar to an English speaker but does not sound the same.

Here først means first in the sense of before anyone else.

So scorer først means:

• scores first
• is the first to score

It does not mean at first here.

That is a common thing for learners to notice, because English first can also appear in expressions like at first, but in this sentence først clearly means first in order.

Glad means happy.

Here it is a predicate adjective, used after bliver:

• bliver glad = becomes happy

So the sentence ends with the state the team ends up in.

With a collective noun like holdet, Danish is treating the team as one unit here:

• hele holdet glad = the whole team happy

In real-life Danish, you may sometimes also hear plural-style thinking with groups of people, but glad is a normal choice in a sentence like this.

Yes. Adding så is possible.

• Hvis min niece scorer først, bliver hele holdet glad.
• Hvis min niece scorer først, så bliver hele holdet glad.

Both are understandable and natural.
The version without så is very common, especially in neutral written Danish.
The version with så can sound a little more explicit or conversational.