La mayoría está de acuerdo.

Because la mayoría means the majority.

In Spanish, you normally use the definite article here, just as in English:

• La mayoría está de acuerdo. = The majority agrees / Most people agree.

Using mayoría by itself is possible only in certain expressions, but not in this sentence.

Because la mayoría is grammatically singular.

Even though it refers to many people, the noun mayoría is treated as one group, so the default verb is singular:

• La mayoría está de acuerdo.

This is very similar to English ideas like the majority is.

A useful point:

• If you say la mayoría de + plural noun, both singular and plural verbs may be heard:
  • La mayoría de los estudiantes está de acuerdo.
  • La mayoría de los estudiantes están de acuerdo.

The singular version treats the group as one unit; the plural version focuses more on the individual members.

Because de acuerdo is used with estar, not ser.

Spanish says:

• estar de acuerdo = to agree / to be in agreement

So:

• Estoy de acuerdo. = I agree.
• Estamos de acuerdo. = We agree.
• La mayoría está de acuerdo. = The majority agrees.

Using ser de acuerdo is not correct.

De acuerdo is a fixed expression meaning in agreement or simply agreeing.

So the sentence is literally something like:

• The majority is in agreement.

But in natural English, you would usually say:

• The majority agrees.
• Most people agree.

Also, de acuerdo can sometimes mean okay / all right, depending on context:

• —Nos vemos a las ocho. —De acuerdo.
• —See you at eight. —Okay.

But in your sentence, it clearly means in agreement.

No. De acuerdo stays the same.

Examples:

• Estoy de acuerdo.
• Ella está de acuerdo.
• Ellos están de acuerdo.
• Las chicas están de acuerdo.

You do not change it to match the subject.

Yes. In many contexts, la mayoría is naturally translated as most people.

So:

• La mayoría está de acuerdo.

can be understood as:

• The majority agrees.
• Most people agree.

The exact English translation depends on how natural you want it to sound.

Yes. You can say la mayoría de... followed by a noun.

Examples:

• La mayoría de los estudiantes está de acuerdo. = The majority of the students agree(s).
• La mayoría de la gente está de acuerdo. = Most people agree.
• La mayoría de nosotros está de acuerdo. = Most of us agree.

This is very common when you want to make the sentence more specific.

Sometimes, but it is not always the best equivalent.

• La mayoría is the most direct way to say the majority / most people
• La mayor parte means the greater part / most of it / most of them

For people, la mayoría is usually the more natural choice:

• La mayoría está de acuerdo.

For things or amounts, la mayor parte is often common too:

• La mayor parte del trabajo ya está hecha.

So for your sentence, la mayoría is the most natural option.

They show where the stress goes.

• mayoría → stress on the final -rí- sound: ma-yo-RÍ-a
• está → stress on the final -tá: es-TÁ

Those written accents are important because without them, the words would either be pronounced differently or be confused with other forms.

For example:

• esta can mean this (feminine)
• está means is

It is neutral and very common.

You can use estar de acuerdo in everyday conversation, in writing, in news, and in formal discussion.

Examples:

• La mayoría está de acuerdo.
• No estoy de acuerdo.
• ¿Estás de acuerdo?

So this is a very useful structure to learn early.

Yes, but estar de acuerdo is the most common and safest everyday choice.

You may also see:

• coincidir in some contexts
• acordar but that usually means to decide / to agree on something together, not simply to share the same opinion

Compare:

• Estoy de acuerdo contigo. = I agree with you.
• Coincido contigo. = I agree with you / I see it the same way.
• Acordamos salir a las ocho. = We agreed to leave at eight.

So in your sentence, está de acuerdo is the standard way to express agrees.