Połowa zespołu zgadza się, że to dobry plan.

Połowa means half.

In this sentence, połowa zespołu means half of the team. This is a very common Polish structure:

• połowa + genitive noun
• so: połowa czego? → zespołu

It works much like English half of the team.

Because połowa requires the genitive case.

So:

• zespół = team
• zespołu = of the team

After words like połowa (half), Polish normally uses the genitive:

• połowa zespołu = half of the team
• połowa tortu = half of the cake
• połowa ludzi = half of the people

So zespołu is there because the phrase means half of the team, not just the team.

Because the grammatical subject is połowa, and połowa is singular.

So Polish treats połowa zespołu as a singular phrase:

• Połowa zespołu zgadza się = Half of the team agrees

That is why the verb is singular:

• zgadza się = agrees

This is similar to how English can also use singular agreement with collective or fractional expressions, depending on style and meaning.

Here zgadza się means agrees.

The basic verb is zgadzać się, which often means:

• to agree
• to be correct / to match, in other contexts

In this sentence it means to agree with an idea or proposal:

• Połowa zespołu zgadza się = Half of the team agrees

Because zgadzać się is the normal dictionary form of this verb when it means to agree.

In Polish, some verbs regularly appear with się. You often just need to learn them as a unit:

• zgadzać się = to agree
• bać się = to be afraid
• uczyć się = to learn

So here:

• zgadza się = agrees

You should think of zgadzać się as the full verb, not as zgadzać plus an optional extra word.

It is the 3rd person singular present tense form of zgadzać się.

Breakdown:

• zgadzać się = to agree
• ja zgadzam się = I agree
• ty zgadzasz się = you agree
• on / ona / ono zgadza się = he / she / it agrees

Since połowa is singular, Polish uses:

• połowa ... zgadza się

Że means that and introduces a subordinate clause.

So:

• Połowa zespołu zgadza się, że...
• = Half of the team agrees that...

It connects the main clause to the content of the agreement.

Very often in Polish, że works just like English that:

• Myślę, że... = I think that...
• Wiem, że... = I know that...
• Uważam, że... = I believe that...

In Polish, to can function like this/that/it is in simple identifying sentences, and jest is often omitted.

So both are possible:

• to dobry plan
• to jest dobry plan

Both mean it is a good plan.

The shorter version is very natural and common, especially in straightforward statements.

Because to-sentences often use the nominative after to, especially in simple identification statements.

So:

• to dobry plan = this/it is a good plan

Both words are nominative:

• dobry
• plan

You may also learn that after być in some contexts, Polish can use the instrumental:

• Jest dobrym planem — but this sounds unnatural here

In this sentence, the natural form is definitely:

• to dobry plan

Yes, that is possible, but it is a bit heavier and less direct.

Compare:

• Połowa zespołu zgadza się, że to dobry plan.
• Połowa zespołu zgadza się z tym, że to dobry plan.

The version with z tym, że is more explicit: agrees with the fact/statement that...

The shorter version is more natural in everyday use.

Not completely. Polish word order is flexible, though the original sentence is very natural and neutral:

• Połowa zespołu zgadza się, że to dobry plan.

You could change the order for emphasis, for example:

• Zgadza się połowa zespołu, że to dobry plan. — possible, but less neutral
• Że to dobry plan, zgadza się połowa zespołu. — very marked, used for emphasis

For learners, the original order is the best one to use.

Yes. Zespół can mean several related things depending on context, such as:

• team
• group
• band
• ensemble

So połowa zespołu could mean:

• half of the team
• half of the group
• half of the band

In your sentence, the intended meaning is clear from context, but it is good to know that zespół is a flexible word.