Mózg jest częścią ciała.

Because after jest in a sentence like X is Y, Polish often uses the instrumental case for Y.

• basic form: część = part
• instrumental singular: częścią

So Mózg jest częścią ciała literally has the structure The brain is a part of the body, with part in the instrumental.

A very common pattern is:

• Jan jest lekarzem = Jan is a doctor
• To jest problemem is possible in some contexts, though less common than other structures
• Mózg jest częścią ciała = The brain is part of the body

Because część usually takes the genitive for the thing it is a part of.

So:

• część ciała = part of the body
• część książki = part of the book
• część miasta = part of the city

The dictionary form is ciało = body, but here it changes to ciała because it is in the genitive singular.

In this sentence:

• Mózg — nominative singular
  It is the subject: the brain
• częścią — instrumental singular
  It is the predicate noun after jest
• ciała — genitive singular
  It depends on częścią: part of the body

So the structure is:

• Mózg = subject
• jest = is
• częścią ciała = a part of the body

Yes, absolutely. Mózg to część ciała is very natural Polish.

The difference is mainly grammatical style:

• Mózg jest częścią ciała
  uses jest
  • instrumental (częścią)
• Mózg to część ciała
  uses to and keeps część in its basic form

Both are correct. A learner will hear both patterns very often.

A rough practical rule:

• X jest Y-em / Y-ą = a very common is pattern
• X to Y = also very common, especially for definitions, explanations, and identifications

Because Polish has no articles.

English needs words like a, an, and the, but Polish does not. So mózg, część, and ciało appear without articles.

Whether English translates them as a brain, the brain, a part, or the body depends on context and meaning, not on a separate Polish word.

A rough guide:

• mózg — roughly moozk
  ó sounds like u in modern Polish
• jest — roughly yest
• częścią — this is tricky; roughly CHEN-shchyom or CHEN-shchom
  The exact sound is hard for English speakers because of cz, ę, ś, and ą
• ciała — roughly CHYA-wa
  ci before a vowel gives a soft ć sound, and ł sounds like English w

A few important sound notes:

• ó = like u
• cz = hard ch-like sound
• ci before a vowel = soft ć
• ł = w
• ą and ę are nasal vowels

Because the subject mózg is singular.

• jest = is for he/she/it and singular nouns
• są = are for plural subjects

So:

• Mózg jest częścią ciała = The brain is part of the body
• Mózgi są częścią... would start a plural sentence: Brains are part of...

The dictionary forms are:

• mózg = brain
• być = to be
• część = part
• ciało = body

In the sentence, two of them change form:

• część → częścią
• ciało → ciała

Looking up dictionary forms is useful because Polish endings change depending on case and number.

They are:

• mózg — masculine
• część — feminine
• ciało — neuter

That matters because Polish nouns change according to gender and case.

In this sentence, the gender does not change the form of jest, because jest is just the 3rd person singular present form of być. But gender is still important for adjectives, past tense forms, and many other sentence patterns.

The most neutral order is:

• Mózg jest częścią ciała.

Polish word order is more flexible than English, so other orders are possible, but they usually add emphasis or sound marked.

For example, something like:

• Częścią ciała jest mózg

is grammatically possible, but it sounds more special or contrastive, not like the normal basic sentence a learner should start with.

So for a plain factual statement, Mózg jest częścią ciała is the best default.

Normally, no — not in standard neutral Polish.

In everyday Polish, some copula-like sentences with to can sound natural without a separate verb in certain contexts, but with this structure you normally say:

• Mózg jest częścią ciała.

Leaving out jest would sound incomplete or stylistically unusual to most learners. So it is best to keep it.