No final de dezembro, metade da equipe já está de férias.

Because no final de is the natural fixed pattern in Portuguese for at the end of.

Here, no is the contraction of em + o, and final is being used as a masculine noun: o final.

So:

• no final de dezembro = at the end of December

Em final de dezembro sounds unnatural in normal Brazilian Portuguese.

Yes. No fim de dezembro is very common and natural.

Both are correct:

• no final de dezembro
• no fim de dezembro

In many contexts, no fim de dezembro sounds a little more conversational, while no final de dezembro can sound slightly more formal or written. But the difference is small.

Because month names usually appear without an article in this kind of expression.

So Portuguese normally says:

• no final de dezembro
• no começo de janeiro
• em fevereiro

Using do dezembro here would sound wrong.

Because da is the contraction of de + a.

The noun equipe is feminine:

• a equipe = the team
• da equipe = de + a equipe = of the team

So metade da equipe literally has the structure half of the team.

Because the grammatical subject is metade, which is singular.

So:

• metade ... está

Even though the idea involves several people, the sentence is structured around half as one unit.

Also, equipe is itself singular, so está is the most natural choice here.

A useful comparison:

• Metade da equipe já está de férias.
• A maior parte da turma já chegou.

In both cases, the main noun controlling the verb is singular.

Já adds the idea of already.

It suggests that, by that point in time, the situation is already true. It can give a sense of:

• something happening earlier than expected
• something that has already become the case by then

So já está de férias means the team members are already on vacation at that time.

Because estar de férias is the normal Portuguese expression for to be on vacation / on leave.

This is a set phrase:

• Estou de férias.
• Ela está de férias.
• Vamos ficar de férias em janeiro.

You should learn it as a chunk: estar de férias.

Because férias is normally a plural-only noun in Portuguese when it means vacation or time off.

So Brazilian Portuguese says:

• as férias
• de férias

Not:

• a féria ✘

This is similar to how some nouns in other languages are normally used in the plural.

It is not absolutely required, but it is very common and helpful.

The phrase No final de dezembro is an introductory time expression. Putting a comma after it makes the sentence easier to read and gives a natural pause:

• No final de dezembro, metade da equipe já está de férias.

Without the comma, the sentence is still understandable, but the comma is a good stylistic choice.

Sometimes, yes, but equipe is the safer and more neutral word here.

• equipe is standard for a work team, staff group, or organized group of people
• time is also used in Brazil, especially in business contexts influenced by English, but it can also strongly suggest a sports team

So in a sentence like this, equipe sounds very natural and standard.

Because equipe is a collective noun: one singular noun that refers to a group.

Just like in English you can say the team or the staff, Portuguese can say:

• a equipe
• a turma
• o grupo

So even though many people are included, the noun itself is grammatically singular.