Η δασκάλα είπε ότι το παιδί είναι ζωηρό στην τάξη, αλλά φέρεται καλά στους άλλους.

Ότι introduces a content clause, like English that:

• Η δασκάλα είπε ότι... = The teacher said that...

In everyday Greek, you may also hear πως in the same role:

• Η δασκάλα είπε πως...

Both are very common here.

Παιδί is a neuter noun in Greek, even when it refers to a boy or a girl in a general sense.

So it takes:

• the neuter article το
• neuter adjective forms

That is why the sentence has:

• το παιδί
• ζωηρό

not ο παιδί or η παιδί, and not ζωηρός / ζωηρή.

Greek adjectives must agree with the noun in gender, number, and case.

Since παιδί is:

• neuter
• singular
• nominative

the adjective must also be neuter singular nominative:

• masculine: ζωηρός
• feminine: ζωηρή
• neuter: ζωηρό

So:

• το παιδί είναι ζωηρό

is the correct agreement.

Because ζωηρό is a predicate adjective, not an adjective directly attached to the noun.

Compare:

• το ζωηρό παιδί = the lively child
  Here the adjective comes directly before the noun, so it is part of the noun phrase.

• το παιδί είναι ζωηρό = the child is lively
  Here the adjective comes after είναι and describes the subject, so no article is needed before it.

This works much like English: we say the child is lively, not the child is a lively.

Here ζωηρό means something like:

• lively
• active
• spirited
• sometimes a bit energetic/restless

In context, especially with στην τάξη, it often suggests a child who is energetic in class and maybe a little hard to keep still, but not necessarily badly behaved overall.

So it is not exactly the same as bad or naughty.

Στην is the contracted form of:

• σε + την = στην

So:

• στην τάξη = in the class / in class / in the classroom

The noun τάξη is feminine, so it uses την.

You will often see these contractions in Greek:

• στο = σε + το
• στη = σε + τη
• στην = σε + την
• στον = σε + τον
• στους = σε + τους

Greek normally uses a preposition here to express in class or in the classroom.

So:

• στην τάξη = in class / in the classroom

English sometimes drops the article or preposition in ways Greek does not. Greek usually prefers the full phrase with σε plus article.

Φέρεται comes from φέρομαι, which in this kind of sentence means:

• to behave
• to conduct oneself
• to treat others

It is one of those Greek verbs that commonly appears in the middle/passive-looking form but has an active meaning in English.

So:

• φέρεται καλά = behaves well

This is very natural Greek.

Yes, it is a very common expression.

• φέρομαι καλά = I behave well
• φέρεται καλά = he/she/it behaves well

It can also mean treats someone well, depending on context.

In this sentence, because of στους άλλους, it has the sense of:

• behaves well toward others
• treats others well

Because καλά is an adverb, and it modifies the verb φέρεται.

• καλός / καλή / καλό = adjective = good
• καλά = adverb = well

So:

• είναι καλό παιδί = he/she is a good child
• φέρεται καλά = he/she behaves well

English also makes a similar distinction between good and well.

Στους is:

• σε + τους = στους

And άλλους means others here.

So:

• στους άλλους = to/toward the others or more naturally toward others

With φέρομαι, Greek often uses σε + accusative for the person someone behaves toward:

• φέρομαι καλά σε κάποιον = I behave well toward someone / I treat someone well

So στους άλλους is exactly what we expect after φέρεται καλά.

Because after σε, Modern Greek usually uses the accusative.

Here the idea is toward others, so Greek says:

• σε τους άλλους → στους άλλους

The base form is:

• οι άλλοι = the others (nominative)
• τους άλλους = the others (accusative)

Since σε takes the accusative, we get στους άλλους.

Greek often omits repeated subjects when they are already clear from context.

So:

• ...ότι το παιδί είναι ζωηρό στην τάξη, αλλά φέρεται καλά στους άλλους.

naturally means:

• ...that the child is lively in class, but behaves well toward others.

The subject of φέρεται is still το παιδί, even though it is not repeated.

You could repeat it for emphasis or clarity:

• ...αλλά το παιδί φέρεται καλά στους άλλους.

But the version without repetition is more natural here.

Greek word order is fairly flexible, though not completely free.

This sentence is natural as written:

• Η δασκάλα είπε ότι το παιδί είναι ζωηρό στην τάξη, αλλά φέρεται καλά στους άλλους.

But some parts could move for emphasis. For example:

• Η δασκάλα είπε ότι στην τάξη το παιδί είναι ζωηρό...
• ...αλλά στους άλλους φέρεται καλά.

These versions shift emphasis slightly, but the basic meaning stays the same.

It can suggest either, depending on context.

• literally: in the classroom
• more naturally in many contexts: in class / during class

So here it probably means the child is lively or energetic when in class, not necessarily only in the physical room.

Greek often allows that kind of overlap.

Yes. Αλλά means but, and it sets up a contrast:

• the child is lively/energetic in class
• but behaves well toward others

So the idea is something like: the child may be active or hard to contain in class, however the child is still considerate or well-behaved with other people.

That contrast is an important part of the tone of the sentence.