Nasz żółw je sałatę bardzo powoli, a królik woli siano niż chleb.

Because sałata is the direct object of je. In Polish, direct objects often go into the accusative case.

• dictionary form: sałata
• accusative singular: sałatę

So:

• Żółw je sałatę = the turtle eats lettuce

This is very common with feminine nouns ending in -a:

• kawa → kawę
• herbata → herbatę
• sałata → sałatę

They are also objects, but their accusative form happens to look the same as the nominative.

• siano is a neuter noun, and neuter singular nouns usually have the same nominative and accusative form.
• chleb is a masculine inanimate noun, and those also usually keep the same form in the accusative singular.

So:

• siano → siano
• chleb → chleb
• but sałata → sałatę

That is why only sałata visibly changes here.

Because żółw is a masculine singular noun, so the possessive adjective must match it.

• masculine singular: nasz
• feminine singular: nasza
• neuter singular: nasze

Examples:

• nasz żółw = our turtle
• nasza sałata = our lettuce
• nasze siano = our hay

In Polish, words like my, your, our often agree with the noun in gender, number, and case.

Because powoli is an adverb, and here we need a word that describes how the turtle eats.

• powolny = slow, as an adjective describing a noun
• powoli = slowly, as an adverb describing a verb

So:

• powolny żółw = a slow turtle
• żółw je powoli = the turtle eats slowly

English makes the same kind of distinction:

• slow vs slowly

Here a links two parts of the sentence and shows a contrast or comparison.

So this sentence is not just:

• and

It is more like:

• and meanwhile
• while
• whereas

So:

• Nasz żółw je sałatę bardzo powoli, a królik woli siano niż chleb.

means something like:

• Our turtle eats lettuce very slowly, while the rabbit prefers hay to bread.

Compare:

• i = simple and
• ale = but
• a = a lighter contrast, often and/while/whereas

Niż means than in comparisons.

In this sentence:

• królik woli siano niż chleb

it means:

• the rabbit prefers hay rather than bread
• or more naturally in English, the rabbit prefers hay to bread

A very common pattern is:

• woleć X niż Y = to prefer X to Y

You can also often see:

• woleć X od Y

For example:

• Królik woli siano niż chleb
• Królik woli siano od chleba

Both express preference, but with od, the second noun changes case:

• chleb → chleba

They are both 3rd person singular present tense verb forms.

• je comes from jeść = to eat
• woli comes from woleć = to prefer

Because the subjects are singular:

• żółw = one turtle
• królik = one rabbit

the verbs are singular too:

• żółw je
• królik woli

A few useful forms:

jeść

• jem = I eat
• jesz = you eat
• je = he/she/it eats

woleć

• wolę = I prefer
• wolisz = you prefer
• woli = he/she/it prefers

It can mean both, depending on context.

Polish does not usually make the same basic present-tense distinction that English does between:

• eats
• is eating

So:

• żółw je sałatę

could mean:

• the turtle eats lettuce
• the turtle is eating lettuce

And:

• królik woli siano niż chleb

is usually a general statement:

• the rabbit prefers hay to bread

Context tells you whether the action is habitual or happening right now.

Yes. Polish word order is more flexible than English because case endings show the grammatical roles.

The sentence as given is natural:

• Nasz żółw je sałatę bardzo powoli, a królik woli siano niż chleb.

But you could move things around for emphasis, for example:

• Nasz żółw bardzo powoli je sałatę
• Sałatę nasz żółw je bardzo powoli

These still mean basically the same thing, but the emphasis changes.

English is much stricter:

• Our turtle eats lettuce very slowly

In Polish, endings often do the job that word order does in English.

Because Polish has no articles.

English uses:

• a
• an
• the

Polish normally does not use separate words for these ideas.

So:

• żółw can mean a turtle or the turtle
• królik can mean a rabbit or the rabbit

You understand which one is meant from context.

That is why the sentence simply says:

• Nasz żółw
• królik and not something equivalent to the turtle or a rabbit.

It is a tricky word for English speakers. A rough guide is:

• żółw ≈ zhoowf

Piece by piece:

• ż sounds like the s in measure
• ó sounds like oo in food
• ł sounds like English w
• final w is pronounced like f here because of final devoicing

So the whole word is roughly one syllable: zhoowf.

It is one of those Polish words that looks harder than it really is once you break it down.

Polish stress is usually on the second-to-last syllable.

In this sentence:

• sa-ŁA-tę
• po-WO-li
• KRÓ-lik
• WO-li

A one-syllable word like żółw just has stress on that only syllable.

This penultimate-stress rule works most of the time in Polish, so it is a very useful default rule for learners.